Answers
Answers:
[tex]\displaystyle \lim_{n \to \infty} \frac{a_n}{b_n} = 6[/tex]
Based on the limit comparison test, the series is convergent
========================================================
Explanation:
As n gets really large, the terms [tex]3^n[/tex] and [tex]3^n-2[/tex] are effectively the same. Taking the limit to infinity of the ratio leads to 1.
In other words,
[tex]\displaystyle \lim_{n \to \infty} \frac{3^n}{3^n-2} = \lim_{n \to \infty} \frac{3^n}{3^n} = 1[/tex]
That -2 doesn't really play a role when n gets very large.
This result is then multiplied by the 6 in the [tex]a_n[/tex] sequence, getting 6 as the final limit we want.
So,
[tex]L = \displaystyle \lim_{n \to \infty} \left(a_n \div b_n\right)\\\\\\L = \displaystyle \lim_{n \to \infty} \left(\frac{6}{3^n-2} \div \frac{1}{3^n}\right)\\\\\\L = \displaystyle \lim_{n \to \infty} \left(\frac{6}{3^n-2} \times \frac{3^n}{1}\right)\\\\\\L = \displaystyle \lim_{n \to \infty} \left(\frac{6*3^n}{3^n-2}\right)\\\\\\[/tex]
[tex]L = \displaystyle 6*\lim_{n \to \infty} \left(\frac{3^n}{3^n-2}\right)\\\\\\L = \displaystyle 6*\lim_{n \to \infty} \left(\frac{3^n}{3^n}\right)\\\\\\L = \displaystyle 6*\lim_{n \to \infty} (1)\\\\\\L = \displaystyle 6*1\\\\\\L = \displaystyle 6\\\\\\[/tex]
Since the limiting value is positive and not infinity, this means that both series [tex]\sum a_n[/tex] and [tex]\sum b_n[/tex] converge or they both diverge.
----------------------------
If we plug n = 2 into the [tex]b_n[/tex] sequence, we get
[tex]b_n = \frac{1}{3^n}\\\\b_2 = \frac{1}{3^2}\\\\b_2 = \frac{1}{9}[/tex]
The first term is a = 1/9
If we plugged n = 3, we would get [tex]b_3 = \frac{1}{27}[/tex]
This shows that the common ratio is r = 1/3
Because -1 < r < 1 is true, we know that the infinite geometric series converges. Therefore, [tex]\sum b_n[/tex] converges. We don't need to find the converging value.
Going back to the limit comparison test, we stated that both [tex]\sum a_n[/tex] and [tex]\sum b_n[/tex] either diverge together or converge together.
We've shown that the b series converges, so the 'a' series must converge as well.
Related Questions
Can someone plz explain to me how to do this !? Geometry
Answers
The scale factor is 3
if you look at the graph its y3 x3 the larger one is y9 x9 if you divide the two you get 3
can you please give brainliest
What is the circumference of a circle that has a radius of 7 m?
Answers
Step-by-step explanation:
you you can use two formulas here either pi d or 2 pi r so when you use pie d which change the radius to diameter by multiplying by two so in this case we will multiply 7 by 2 to get 14 then use the formula so is 22/7 * 14 to get 44
How many edges are there on a cylinder?
Answers
Answer:
There are 0 number of edges on a cylinder
Find the area, in square units, of ABC plotted below.
A(0,7)
B(7,-2)
D(2, -3)
C(-3,-4)
Answers
So A=52 square units
And the brackets was absolute value
The area of the triangle ABC for the considered triangle plotted in the considered image is 66.5 sq. units approximately.
What is the distance between two points ( p,q) and (x,y)?The shortest distance(length of the straight line segment's length connecting both given points) between points ( p,q) and (x,y) is:
[tex]D = \sqrt{(x-p)^2 + (y-q)^2} \: \rm units.[/tex]
The coordinates of the points A, B, C, and D in the given figure are:
A(0, 7)B( 7,-2)C(-3, -4)D(2, -3)Finding the length of the line segments AD and CB, which will be the distance between A and D, and C and B respectively.
Thus, we get:
Length of line segment AD = |AD| = distance between A and D = [tex]\sqrt{(0-7)^2 + (7-(-2))^2} = \sqrt{7^2 + 9^2} = \sqrt{130} \: \rm units.[/tex]
Similarly, we get:
|CB| = [tex]\sqrt{(-3-7)^2 + (-4-(-2))^2} = \sqrt{10^2 + 6^2} = \sqrt{136} \: \rm units.[/tex]
If we take CB as the base of ABC triangle, then as AD is perpendicular on CB, and touches the peak of the triangle ABC from its base, so AD is height of the triangle.
Thus, as we know know that:
Height's measurement of ABC = |AD|= [tex]\sqrt{130} \: \rm units[/tex]Base length of ABC = |BC| = [tex]\sqrt{136} \: \rm units[/tex]Thus, the area of the triangle ABC is:
[tex]A = \dfrac{base \times height}{2} = \dfrac{\sqrt{130} \times \sqrt{136}}{2} \approx 66.5 \: \rm unit^2[/tex]
Thus, the area of the triangle ABC for the considered triangle plotted in the considered image is 66.5 sq. units approximately.
Learn more about distance between two points here:
brainly.com/question/16410393
#SPJ2
Rewrite it as a function and isolate Y.
Answers
Answer: y= -2x + 12
or f (y ) = 6 - [tex]\frac{y}{2}[/tex]
Step-by-step explanation:
just subtract the 2x to get the y alone
which type of statement has the form if a then B?
Answers
Answer:
A Conditional Statement
Answer:
Conditional would have that form.
Ms. Smith bought a 5 pound bag of candy for her 6 grade classroom. She gave away 2 pounds of candy to her students during the first unit of
instruction and ate 6 ounces of candy during planning.
How many ounces of candy does Ms. Smith still have in her bag?
Note: (1 pound = 16 ounces)
A 38 ounces
o
B. 42 ounces
O c. 48 ounces
D. 54 ounces
Answers
Answer:
42 ounces or B
Step-by-step explanation:
5 pounds - 2 pounds=3 pounds
3 pounds=48 ounces
48 ounces-6 ounces=42 ounces
Bender Electronics buys keyboards for its computers from another company. The keyboards are received in shipments of 100 boxes, each box containing 20 keyboards. The quality control department at Bender Electronics first randomly selects one box from each shipment and then randomly selects 5 key boards from that box. The shipment is accepted if not more than 1 of the 5 keyboards is defective. The quality control inspector at Bender Electronics selected a box from a recently received shipment of keyboards. Unknown to the inspector, this box contains 6 defective keyboards.
Round your answers to four decimal places.
a. What is the probability that this shipment will be accepted?
P(shipment accepted)=
b. What is the probability that this shipment will not be accepted?
P(shipment not accepted)=
Answers
Answer:
a
[tex]P(shipment\ accepted) =0.6337 [/tex]\
b
[tex]P(shipment\ not\ accepted)= 0.3663 [/tex]
Step-by-step explanation:
from the question we are told that
The number of boxes N = 100
The number of keyboard in each box is k = 20
The sample size is n = 5
Generally the number of ways of selecting 1 keyboard from the 5 selected keyboard is mathematically represented as
[tex]G = \ ^{5}C_1[/tex]
Here C stands for combination (Hence in the question we will be making use of the combination functionality in our calculator )
Generally the number of ways of selecting 0 keyboard from the 5 selected keyboard is mathematically represented as
[tex]H = \ ^{5}C_0[/tex]
Generally the number of ways of selecting 5 keyboard from the 20 keyboards is mathematically represented as
[tex]F = \ ^{20}C_5[/tex]
Generally the number of ways of selecting 5 keyboard from the 15 keyboards is mathematically represented as
[tex]W = \ ^{15}C_5[/tex]
Generally the number of ways of selecting 5 keyboard from the 15 keyboards is mathematically represented as
[tex]V = \ ^{15}C_4 [/tex]
Generally the probability that a shipment will be accepted is mathematically represented as
Probability of 0 defect out of 5 + Probability of 1 defect out of 5
Now
Probability of 0 defect out of 5 is mathematically represented as
[tex]P(A_1) = \frac{H*W }{ F}[/tex]
=> [tex]P(A_1) = \frac{1 *3003 }{ 15504}[/tex]
=> [tex]P(A_1) = 0.1937[/tex]
And Probability of 1 defect out of 5 is mathematically represented as
[tex]P(A_2) = \frac{ G * V}{ F}[/tex]
=> [tex]P(A_2) = \frac{ 5 * 1365}{15504}[/tex]
=> [tex]P(A_2) = 0.440[/tex]
Generally the probability that a shipment will be accepted is mathematically represented as
[tex]P(shipment\ accepted) =0.1937 + 0.440[/tex]
=> [tex]P(shipment\ accepted) =0.6337 [/tex]
Generally the probability that this shipment will not be accepted is mathematically represented as
[tex]P(shipment\ not\ accepted)= 1 -P(shipment \ accepted)[/tex]
[tex]P(shipment\ not\ accepted)= 1 - 0.6337 [/tex]
[tex]P(shipment\ not\ accepted)= 0.3663 [/tex]
Find x and y. Give reasons to justify your solution. AB, CD, EF, and GH are straight lines.
Answers
Answer:
X= 32 Y= 35
Step-by-step explanation:
We know FOB is parralel to AOE meaning x= 32
also, COH = 90 so GOD is also 90.
a straight angle is 180, so
23+90+x or 32= 145,
180-145=35,
y=35
Answer:
X=32
Y=35
Step-by-step explanation:
We know x is 32 because FOB is parrallel to AOE.
We also know that DOG is 90 because COH is 90, and parallel to DOG
So, we can do:
90 + 23 + 32 =145
180-145=35, which is Y
Question 4
5 pts
4. Cassie has 45 marbles. Abdul has m If Cassie has 9 times as many
marbles as Abdul. Choose the equation that correctly represents the
number of marbles Abdul has.
O 9 x m = 45
O 45 - 9 = m
O C. 9+ m = 45
O D. 9 x 45 = m
Answers
Answer:
8 x m = 45
Step-by-step explanation:
cassie has 9 times which means multiplcation so its the first one
Write 257% as decimal
Answers
Answer:
please mark brainliest!
Step-by-step explanation:
2.57
Answer:
2.57
Hope this helps! Mark me brainliest
god bless!
Which angle are vertical to each other
Answers
QUESTION:
An airplane flies with a constant speed of 660 miles per hour. How long will it
take to travel a distance of 2475 miles?
Answers
Answer:
5643
Step-by-step explanation:
you add them together then you divide
Three times two less than a number is greater than or equal to five times the number. Find all of the numbers that satisfy the given conditions.
Let n = a number. Choose the inequality that represents the given relationship.
Answers
P.S Make sure to put a line under the inequality sign to represent greater than or equal to ;)
Answer:
D on edge
3(n – 2) ≥ 5n
Step-by-step explanation:
the next question's answer is B
Solve for S
P=4s
Please answer!!!!
Answers
Answer:
b
Step-by-step explanation:
divide both sides of the equation by 4 to leave s by itself
if 6 pounds of apples cost $9, how much would 21 apples cost?
Answers
Explanation:
You can do 6+6 3 time and that equals 27 dollars, and you have one more so 9 divided by 2 is 4.5 so if you add that you get 31.5
Type the correct answer in each box. Use numerals instead of words. For this question, any answer that is not a whole number should be entered as a fraction in simplest form, using / as the fraction bar, or as a decimal number rounded to the hundredths place. The point P has a value of and is represented with a point on the top number line. The point R has a value of and is represented with a point on the bottom number line. If the value of point P is and |Q| is , then the greatest value of P + Q is , and the least value of P + Q is . If the value of point R is and |S| is 2, then the greatest value of R + S is , and the least value of R + S is . Reset Submit
Answers
Answer:
Step-by-step explanation:
Since we are not given the value of P, |Q|, R and S, we can as well assume values for them for the sake of this question.
Let P = 5, |Q| = 6, R =7 |S| = 2
Note that since Q and S are in modulus sign, they can return both positive and negative values.
P+Q = 5 + 6 (note that the positive value of Q is used since we need the greatest value of P+Q)
P+Q = 11
Hence the greatest value of P+Q is 11
For the least value of P+Q, we will use the negative value of Q as shown
P+Q = 5+(-6)
P+Q = 5-6
P+Q = -1
Hence the least value of P+Q is -1
Similarly:
R+S = 7 + 2 (note that the positive value of S is used since we need the greatest value of R+S)
R+S = 9
Hence the greatest value of R+S is 9
For the least value of R+S, we will use the negative value of S as shown
R+S = 5+(-2)
R+S = 5-3
R+S = 2
Hence the least value of P+Q is 2
NOTE THAT THIS ARE ASSUMED VALUES. ALL YOU NEED IS TO PLUG IN THE VALUES OF P, Q and R THAT YOU HAVE IN CASE THE VALUES DIFFERS.
Please answer this correctly without making mistakes
Answers
Answer:
89%
Step-by-step explanation:
There are 100 units within the shape and 89 of them are painted so 89% is orange
is this correct or not
Answers
Answer:
yes it is u did a good job
Solve the following equation algebraically. Show your work.
6=x+23
Answers
Answer: 23+x=6
-23 -23
1x/1 -17/1
x=-17
Step-by-step explanation:
Answer:
Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation :
-6*x-(23)=0
Step by step explanation :
Pulling out like terms
Pull out like factors :
-6x - 23 = -1 • (6x + 23)
Solving a Single Variable Equation:
2.1 Solve : -6x-23 = 0
Add 23 to both sides of the equation :
-6x = 23
Multiply both sides of the equation by (-1) : 6x = -23
Divide both sides of the equation by 6:
x = -23/6 = -3.833
Therfor the answer is : x = -23/6 = -3.833
what is the sales tax if a $9,895 purchase will have $809.41 of sales tax added to it? round to one decimal place
Answers
Answer:
8.2%
Step-by-step explanation:
9,895x = 809.41
x = 0.08179 or 8.2%
I need help in math please I am not able to figure these out, I will give you the brainlest and thank you.
Answers
Answer:
A. -7 A2. -7
B.-14 B2. 2
C.-14 C2.14
D. 1 D2. -7
9514 1404 393
Answer:
a. -7, -7
b. -14, 2
c. -14, -14
d. 1, -1
e. misuse of the associative property leads to different results
Step-by-step explanation:
Your calculator (or a spreadsheet) can figure these easily.
a. -12 +(-4 +9) = 12 +5 = -7
(-12 +(-4)) +9 = -16 +9 = -7
__
b. (14 -20) -8 = -6 -8 = -14
14 -(20 -8) = 14 -12 = 2
__
c. (14 +(-20)) +(-8) = -6 -8 = -14
14 +(-20 +(-8)) = 14 +(-28) = -14
__
d. -1 -(-1 +(-1)) = -1 -(-2) = -1 +2 = 1
(-1 -(-1)) +(-1) = (-1+1) -1 = 0 -1 = -1
__
e. The associative property works for addition. When the associative property is used to rearrange subtraction problems, the minus signs need to be kept with the numbers, as in (c). That is, the problem needs to be expressed as a sum of signed numbers.
In (d), the term -(-1 +(-1)) was broken in the middle when the sum was rearranged for the second expression. Only terms in the same level of parentheses can be rearranged by the associative property.
A line has a slope of 9 what is the slope of a line it is parallel to this line? *
9
-9
1/9
-1/9
Answers
Answer: 9
Step-by-step explanation: Parallel lines have the same slope.
So a line parallel to this would also have 9 as its slope.
find the perimeter of a circle whose diameter is 12.6 cm please help and show working
Answers
Answer:
39.584034 cm
Step-by-step explanation:
Firstly find the radius, 6.3 cm. Then plug into the formula, 2πr.
I used 3.14159 as pi.
work:
2 * 3.14159 * 6.3
6.28318 * 6.3
39.584034
13/20 of a number is what percentage of that number?
Answers
Answer:
65%
Step-by-step explanation:
Mikhail draws triangles ABC and FED, as shown below, and claims that the two triangles are similar but not congruent.
Select all methods that can be used to justify the claim.
show that 2C 2D and that all corresponding sides are congruent
show that 2C 2D and that all corresponding sides are proportional
show that a sequence of rotations, reflections, and translations carries triangle ABC onto triangle FED
show that a sequence of rotations, reflections, translations, and dilations carries triangle ABC onto triangle FED
Answers
Answer:
First definitions:
Two triangles are congruent if the corresponding sides are all the same length (one triangle can be a rotation, translation or reflection of the other)
Two triangles are similar if the corresponding interior angles are equal and the corresponding sides are proportional. (so one triangle can be a rotation, translation, reflection or contraction/dilation of the other)
You can notice that two congruent triangles are similar, but two similar triangles are not necessarily congruent.
Then two methods to show that the triangles are similar but not congruent are:
1) show that a sequence of rotations, reflections, translations, and dilations carries triangle ABC onto triangle FED
If we have a dilation, then the sidelengths of the corresponding sides can not be equal, wich implies that the triangles are not congruent.
2) show that 2C 2D and that all corresponding sides are proportional
If the sides are proportional, then it is similar, but not congruent.
please help
Select the correct answer.
In 14 days, the daily high temperature in Cedar Hills dropped by 16.8 degrees Fahrenheit. What is the average daily rate of change in the high temperature in degrees Fahrenheit?
A.
+2.2
B.
+1.2
C.
+1.1
D.
-1.2
E.
-2.2
Answers
Answer:-1.2 Degree Fahrenheit.
Step-by-step explanation:
Since,
The average daily changes, total changes/number of days
Here,
The total changes = - 16.8° F ( - sign shows the decreasing )
And, the number of days = 14
Hence,
⇒ The average daily rate of change in the high temperature in degrees Fahrenheit is -1.2° F.
-16.8 / 14 = - 1.2 per day
[tex]lx+3l \leq 5[/tex]
Answers
9514 1404 393
Answer:
-8 ≤ x ≤ 2
Step-by-step explanation:
We assume you intend the absolute value equation ...
[tex]|x+3|\le5\\\\{-}5\le x+3\le5\qquad\text{rewrite as a compound inequality}\\\\\boxed{{-}8\le x\le2}\qquad\text{subtract 3}[/tex]
Simplify [tex]\frac{14^{15} }{14^{5} }[/tex]:
A. [tex]1^{3}[/tex]
B. [tex]1^{10}[/tex]
C. [tex]14^{3}[/tex]
D. [tex]14^{10}[/tex]
Answers
Answer:
The answer is D 14^10
Answer:
A
Step-by-step explanation:
30% of what equals 600
Answers
Answer: it equals 180 hope it helps
Answer:
180
Step-by-step explanation:
30% × 600 =
(30 ÷ 100) × 600 =
(30 × 600) ÷ 100 =
18,000 ÷ 100 =
180
Hope this helps!! Good luck on your assignment!