Answers
You can first condense the series to make it simpler to study. If n is odd, then n = 2k - 1, and if n is even, then n = 2k for some k ≥ 1. So for each k, you can pair up the k-th terms of the odd- and even-indexed series.
odd:
[tex]\dfrac1{3^{\frac{n+3}2}}=\dfrac1{3^{k+1}}[/tex]
even:
[tex]\dfrac1{3^{\frac n2}}=\dfrac1{3^k}[/tex]
So the series can be re-indexed as
[tex]\displaystyle\sum_{n=1}^\infty a_n=\sum_{k=1}^\infty a_k=\sum_{k=1}^\infty \left(\frac1{3^{k+1}}+\frac1{3^k}\right)=\sum_{k=1}^\infty\frac4{3^{k+1}}[/tex]
By the root test, the series converges, since
[tex]\displaystyle\lim_{k\to\infty}\sqrt[k]{\left|\frac4{3^{k+1}}\right|}=\frac13\lim_{k\to\infty}\left(\frac43\right)^{\frac1k}=\frac13<1[/tex]
Related Questions
For what values of a does the equation ax^2+x+4=0 have only one real solution?
Answers
Answer:
1/16
Step-by-step explanation:
To have one real solution, the discriminant must be 0.
b² − 4ac = 0
1² − 4a(4) = 0
1 − 16a = 0
a = 1/16
If you are self-employed, you don't have to pay FICA on all your salary, just on 92.35% of it. If your salary is $128,255 what is your total monthly contribution (FICA is 15.3%)?
Answers
Answer:$1,510
Step-by-step explanation:
PLEASE HELP MEEE!! I will give brainliest!
Find a counterexample to show that the following statement is false. Thrice a number is always greater than the number.
Answers
Answer:
a
Step-by-step explanation:
3 times 0 is still zero so its not grater
50 points!
What is a quartic function with only the two real zeroes given? x = 5 and x = 1
y = -x4 - 6x3 + 6x2 - 6x + 5
y = x4 + 6x3 - 6x2 + 6x - 5
y = x4 - 6x3 + 5x2 - 6x + 6
y = x4 - 6x3 + 6x2 - 6x + 5
Answers
Answer
y = x4 - 6x3 + 6x2 - 6x + 5
Step-by-step explanation:
usually factor and set each factor = to 0 and solve for x...so we will unsolve it.
x=5 and x=1 If you meant quartic. Quartic is a function where the leading term has a forth power. So, you can multiply the quadratic function times any other quadratic function that only gives you complex answers...the easiest would be
y = x4 - 6x3 + 6x2 - 6x + 5
Answer:
y = x4 - 6x3 + 6x2 - 6x + 5
Step-by-step explanation:
Hope this helps
Type the correct answer in each box Functions h and k are inverse functions, and both are defined for all real number Using this relationship, what is the value of each function composition? (h*k)(3)
Answers
The value of the given composite functions would be,
1) (h o k)(3) = 3
2) (k o h)(-4b) = -4b
How to interpret Inverse Functions?
When two functions are inverses, then each will reverse the effect of the other.
For the functions f and g, we can say that;
(f o g)(x) = x and (g o f)(x) = x
For the given example,
The functions h and k are inverse functions.
Thus, for any real input value 'x',
(h o k)(x) = x and (k o h)(x) = x
So, the value of the given composite functions would be,
1) (h o k)(3) = 3
2) (k o h)(-4b) = -4b
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What is the value of X? GIVING BRAINLIEST FOR WHO ANSWERS BY 5 MINUTES.
Answers
Answer:
15
Step-by-step explanation:
triangle is isosceles
solve the equation
(-7) (-5)
Answers
Approximately 18% of the population of California is 70 years or older. In a random sample of 4, what is the provability for 3 of these people to be older than 70 years old.\
Answers
Answer:
The correct response will be "0.01913".
Step-by-step explanation:
According to the question,
p - P(70 years or older)
= 0.18
n = 4
X = no. of individuals who are older than 70 years
Now,
∴ [tex]P(X=r)=n_C_r \ p^r(1-p)^{n-r}[/tex]
∴ [tex]P(X=3)=4_C_3(0.18)^3(1-0.18)^{4-3}[/tex]
[tex]=4\times (0.18)^3(0.82)^1[/tex]
[tex]=0.01913[/tex]
PQR is a right-angled triangle.
Work out the size of angle PQR.
Give your answer correct to 1 decimal place.
Total marks: 3
Answers
Answer:
67.4
Step-by-step explanation:
In picture listed above.
Brainliest Appreciated.
The measure of the angle PQR will be 67.4 degree.
What is mean by Triangle?
A triangle is a three sided polygon, which has three vertices and three angles which has the sum 180 degrees.
Given that;
Sides of a triangle are 13 cm , 5 cm, and 12 cm.
And, The angle PRQ = 90 degree.
Now,
Find the measure of angle PQR as;
The triangle PQR is a right triangle and PQ = 13 cm and PR = 12 cm.
Let measure of an angle PQR = θ
So, We can formulate;
sinθ = PR/PQ
sinθ = 12/13
θ = 67.4 degree.
Thus, The measure of the angle PQR will be 67.4 degree.
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which statement best describes the range of f(x)=-2
Answers
The zoo is creating a new tank for some of its fish. The zoo wants the tank to be a cube and be able to hold 3,375 cubic feet of water. What equation would you solve to find the length of each side of the tank?
Answers
Answer:
³√3375
Step-by-step explanation:
Hope this will help guys
Evaluate 13 + 6/y when y = 6
Answers
Answer: 14
Step-by-step explanation: According to PEMDAS you do division first so if y=6 then you do 6/6=1. Then add 13+1
Answer:
14
Step-by-step explanation:
13 + 6/y
13 + 6/(6)
13 + 1
14
18% of the cars in the parking lot are blue.If there are 150 cars in the parking lot,how many cars are blue
Answers
Answer:
Step-by-step explanation:
14
A line contains the points A, B, C, and D. Point B is
between points A and C. Point D is between points C
and B. Which of the following inequalities must be true
about the lengths of these segments?
F. BC < AB
G. BD < AB
H. BD < CD
J. CD < AB
K. CD
Answers
Answer:
a
Step-by-step explanation:
aa
Can Someone help a girlll outttt pleasee
364÷2853.76 < I will appreciate it !!! <3
Answers
Answer:
364 divided by 2853.76 = 0.13 or 0.128
Step-by-step explanation:
25 POINTS! factor the trinomial:[tex]x^2-2x-2[/tex]
Answers
( x − 1 + i ) ( x − 1 − i )
Step-by-step explanation:
_____________ (x-1+i)(x-1-i)
What is the slope of the line?answer
Answers
Answer:
1
Step-by-step explanation:
the rise is 1
and the walk is 1
please help will give brianliest
Answers
Answer:
I helped
Step-by-step explanation:
you okay do can I get some points cuh
Answer:
with what?? >_>
what is the graph of 4x + 8y = 16?
Answers
Answer:
See attachment for what the graph looks like.
Step-by-step explanation:
When you graph these equations, convert 4x+8y=16 into slope-intercept form, which should be y= -1/2x+2.
In this case, 2 is the y-intercept, the part of the line that intercepts with the y-axis, with a negative (goes downward) slope of 1/2.
The line should intersect at (0,2) and have a slope of -1/2.
The x-intercept of the line is at 4 and the y-intercept of the line is at 2. Then the graph is sketched below.
What is a linear equation?A connection between a number of variables results in a linear model when a graph is displayed. The variable will have a degree of one.
The linear equation is given as,
x/a + y/b = 1
Where 'a' is the x-intercept of the line and 'b' is the y-intercept of the line.
The equation of the line is given below.
4x + 8y = 16
Convert the general form of the line into an intercept form. Then we have
4x + 8y = 16
x/4 + y/2 = 1
The x-intercept of the line is at 4 and the y-intercept of the line is at 2. Then the graph is sketched below.
More about the linear equation link is given below.
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Samir usually drink 3 cups of coffee in the morning how many liters of coffee does he drink round
Answers
Answer:
0.709765 liters
Step-by-step explanation:
Who is the most powerful undertale character
Answers
Answer:
Asriel Dreemurr
Step-by-step explanation:
Answer:
clearly the gay robot
hes my favorite <3
is {3/4,3} a solution to y-8x=3
Answers
3 - 8(3/4) = 3
3 - 6 = 3
3 = 9
False, so no. (3/4,3) is not a solution to the equation.
Answer:
No it is not a solution
Step-by-step explanation:
If you put 3/4 in x you get
y-8*3/4=3
y-6=3
y=9
Wich is not equal to 3
ILL GIVE BRAINLIEST!
HELP ASAP!
Select the correct answer.
Which equation represents the line that is parallel to
y = 3/7x + 11 and passes through (-21,42)?
A. y = -7/3x - 7
B. y = -7/3x + 77
C. y = 3/7x - 39
D. y = 3/7x + 51
Answers
Answer: y = 3/7x + 51
Step-by-step explanation:
The following is a conversion table for hours and minutes. Which numbers belong in the hours column?
1, 2, 3
1, 2, 4
2, 3, 4
2, 5, 6
Answers
Answer:
Lesson 2 and metric conversions from Module 2. ... Problem 2: Convert hours to minutes. ... of minutes in one hour. How many minutes are in an hour? 0. 1. 2. 3. 4. 5. 6. 7. 8.
The complete table is given below. Then the correct option is C.
Hours Minutes
2 120 3 180 4 240What is Algebra?The analysis of mathematical representations is algebra, and the handling of those symbols is logic.
The following is a conversion table for hours and minutes.
We know that in one hour, there are 60 minutes.
In two hours, there are 120 minutes.
In three hours, there are 180 minutes.
Similarly, in four hours, there are 240 minutes.
Then the complete table is given below.
Hours Minutes
2 120
3 180
4 240
Then the correct option is C.
The complete question is given below.
The following is a conversion table for hours and minutes. Which numbers belong in the hour's column?
Hours Minutes
120
180
240
More about the Algebra link is given below.
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YALLLL PLEASE HELP MEEE ASAP PLEASE PLEASE HELP I WIIIL MAKR BRANLIEST TO HOWEVER GIVES THE ANSWER FIRST AND IS CORRECT!!!!
Write the equation of the line that has a slope of 4 and goes through the point (,-4,6)
Answers
Answer:
y=4x-10
Step-by-step explanation:
Write the slope intercept form of the equation of each line. Help me plz
Answers
PLZ Help Urgent. 15 POINTS, BRAINLY Guaranteed.
Plz Answer honestly or you will be reported.
Evaluate.
(2/7)^3
A: 8/343
B: 8/7
C: 3/343
D: 6/7
Answers
Answer:
8/343
so A
Step-by-step explanation:
Write the equation in slope-intercept form.
- 4x – 10y = -7
Answers
Answer:
The answer will be in the form y=mx+b
y= - [tex]\frac{2}{5}[/tex] x + [tex]\frac{7}{10}[/tex]
Brainliest please
The equation of a line is an algebraic form of representing the set of points, which together form a line in a coordinate system.
The equation of -4x - 10y = -7 in slope-intercept form is
y = (-2/5)x + (-7/10)
What is slope intercept form?The equation of a line is an algebraic form of representing the set of points, which together form a line in a coordinate system.
The equation of a line in slope intercept form is given by:
y = mx + c
m = slope
c = y-intercept
We have,
-4x - 10y = -7
Add 4x on both sides.
-4x - 10y + 4x = 7 + 4x
-10y = 7 + 4x
Multiply -1/10 on both sides.
y = -1/10 ( 7 + 4x )
y = -7/10 - (4/10)x
y = (-2/5)x + (-7/10)
Thus the equation of -4x - 10y = -7 in slope-intercept form is
y = (-2/5)x + (-7/10)
Learn more about the equation of a line here:
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BRAINLIEST if you get it correctly and fastest
Answers
Answer:
The third one
Step-by-step explanation:
IF THIS GETS TAKEN DOWN IMA SCREAM
Solve the inequality -5(x-7)<15 algebraically for x
Answers
Answer:
x>4
Step-by-step explanation:
trust