Consider the series
[infinity]
∑ (-1)^n (x+1)^n/ (n+1)!
n=0
a. Find the series' radius and interval of convergence.
b. For what values of x does the series converge absolutely?
c. For what values of x does the series converge coditionally?
(a) If
[tex]f(x)=\displaystyle \sum_{n=0}^\infty (-1)^n \frac{(x+1)^n}{(n+1)!}[/tex]
then by the ratio test, the series converges for all x, since
[tex]\displaystyle \lim_{n\to\infty} \left| \frac{ (-1)^{n+1} \frac{(x+1)^{n+1}}{(n+2)!} }{ (-1)^n \frac{(x+1)^n}{(n+1)!} } \right|=\lim_{n\to\infty}\frac{|x+1|}{n+2}=0[/tex]
so the series radius of convergence is ∞ and the interval of convergence is (-∞, ∞).
(b) The series converges everywhere absolutely, because the ratio test for
[tex]\displaystyle \sum_{n=0}^\infty \frac{|x+1|^n}{(n+1)!}[/tex]
also shows the radius of convergence is ∞.
(c) The series converges absolutely, so conditional convergence is moot.
what comes first on a slope x or y
Answer:
x
Step-by-step explanation:
Answer:
when you are graphing do x first
Step-by-step explanation:
The slope of a line is usually represented by the letter m. (x1, y1) represents the first point whereas (x2, y2) represents the second point. It is important to keep the x-and y-coordinates in the same order in both the numerator and the denominator otherwise you will get the wrong slope.
Round 6.487 and 2.049 to the hundredths place. What is the sum of the rounded numbers? *
Answer:
8.54
Step-by-step explanation:
If thousandth's place is ≥ 5 , then add 1 to the hundredth place.
6.487 = 6.49
2.049 = 2.05
6.487 + 2.049 = 6.49 + 2.05 = 8.54
Scarlett is playing a video game. She spends 900 minerals to create 18 workers. Each worker costs the same number of minerals.
So you would do 900÷18 to get the amount each worker is worth, which would be 50 minerals.
Answer: m=50w
Step-by-step explanation:
When you divide 900 by 18, you get 50.
Since we are trying to find the amount of minerals per worker, m is the first variable. w is the second because that is the number of workers you can get with the minerals Scarlett has.
0=p-27h/17+h solve for p
Answer: The answer is p=10h/17.
Step-by-step explanation: You'll need to solve for p by simplifying the both sides of the equation, and then isolating the variable.
Describe a situation where it would be beneficial to round decimals to the nearest dollar explain why you would use rounding in that situation
Answer:
3units/ 5 feet = 60 units/ 100 feet3 units/ 5 feet = 18 units/ 30 feetthe dimensions of the scale drawing are 60 units by 18 units
Step-by-step explanation:
please dont answer with random things i actually need the answer
Which of these inequalities are equivalent to r > -11?
Check all that apply.
-r -33
-3r 33
Random answers get reported
Answer:
A,C, and D
just did the assignent
Answer:
ACD
Step-by-step explanation:
Select all that apply
A class has 7 boys and 10 girls. Select all associated ratios for this class.
10:3
7:3
17:5
7:17
10:7
10:17
7:10
3:7
happy thanksgiveing <3
Answer:
ty!
Step-by-step explanation:
why we develop corporations
Answer:
Answer -The main reason for forming a corporation is to limit the liability of the owners.
Step-by-step explanation:
4 Jarome needs to have at least $150 to open his own checking account. He has already saved $30 and plans to earn more money by mowing six lawns this week. Use a piece of paper to write and solve an inequality to determine the minimum amount of money Jarome needs to charge for each lawn he mows this week so he can open his own checking account at the end of the week. Jarome needs to charge at least $___ for each lawn he mows this week.
Answer:
how much does he get from each house
Step-by-step explanation:
PLEASE HELP
Which is the function represented by the table?
Answer:
f(x) = 4x
Step-by-step explanation:
-2 x 4 = -8
-1 x 4 = -4
0 x 4 = 0
1 x 4 = 4
Elise sent 6 postcards during her vacation. Deandre sent fewer postcards than Elise. Plot the points on the provided number line that could represent the number of postcards Deandre sent during his vacation.
Answer:
im pretty sure it's 8 I'll make sure to do the math right again but I'm pretty sure it's 8
plot the points on 5 , 4 , 3, and 2
PLS ANSWER FAST
solve for the unknown...
3^x = 9^x+5
PLS HELP IF YOU WANT
Chelsea takes the bus to school, but she walks home. The bus travels to the school at an average speed of 45 miles per hour. While going home from school, Chelsea walks at a speed of 2.5 miles per hour.
In total, she takes 1 hour to travel to school and back. If t is the time it takes to go to school by bus, the equation that will help find the time it takes Chelsea to get to school on the bus is ANSWER1
. The equation will have ANSWER2
PLS ANSWER ANSWER 1 AND 2
Answer:45 * t = 2.5 * (1-t)...the equation will have one solution.
Step-by-step explanation:
For this case, the first thing you should know is:
d: v * t
Where,
d: distance
v: speed
t: time
To go to school by bus we have:
d = 45 * t
To return from school we have:
d = 2.5 * (1-t)
how the distance is the same:45 * t = 2.5 * (1-t)
....................... Plz
Answer:
2/5 (x-1)=15 (x=7)
7 (1+3m)=49 (m=2)
Answer:
1. x=77/2
2. m=2
Step-by-step explanation:
A piece of iron has a volume of 15cm^3 and a mass 27g.calculate the density of iron in kg/m^3
Answer:
density = mass/volume or mass = density * volume, so 7.86 * 15 = 117.9 grams
Step-by-step explanation:
what is the slope of every line perpendicular to (0,1) and (2,-4)
Answer:
m=-[tex]\frac{-5}{2}[/tex]
Step-by-step explanation:
m = [tex]\frac{y{2}-y{1} }{x2-x1}[/tex]
[tex]m=\frac{-4-1}{2-0}[/tex]
[tex]m=\frac{-5}{2}[/tex]
Which of the following sets of ordered pairs (x,y) is NOT a function of x?
A.
{(0,1),(1,0),(1,1)}
B.
{(0,0),(1,1),(2,2)}
C.
{(0,0),(1,1),(2,1)}
D.
{(0,1),(1,1),(2,1)}
Answer:
The answer is A.
Step-by-step explanation:
hope this helps
what is negative 3 and one fourth minus 3 and one fourth
Answer:
-6 1/2
Step-by-step explanation:
Answer:
-6.5
Step-by-step explanation:
pls give me brainiest
Write the expression in complete factored form.
4b2(x + 2) + c(x + 2) =
Answer:4b+c2-x2=8
Step-by-step explanation:
find the distance between (-8,7) and (13,-1)
Answer:
22.4722
Step-by-step explanation:
To answer this question we need to use the distance formula. The distance formula is as follows:
[tex]d = \sqrt{(x2 - x1)^2+(y2 - y1)^2}[/tex]
Now, let's identify what each variable is:
x2 = 13
x1 = -8
y2 = -1
y1 = 7
Next, let's put these into the equation:
[tex]d = \sqrt{(13 - (-8))^2 + (-1 -7)^2}[/tex]
Time to solve the equation:
[tex]d = \sqrt{(21)^2+(-8)^2} \\d = \sqrt{441 + 64} \\d = \sqrt{505} \\d = 22.4722[/tex]
Therefore, the distance between the points of (-8,7) and (13,1) is 22.4722.
I hope this helps!!
- Kay :)
Louis and Max are contestants in a jellybean-eating contest. Louis eats 18 jellybeans
in 30 seconds. Max eats 24 jellybeans in 40 seconds.
Answer: They ate at the same pace.
Step-by-step explanation: assuming you want to know who ate more faster you can do 18 / 30 and 24 / 4 to find out who ate more in 10 seconds each.
18 / 3 = 6 and 24 / 4 = 6. So they ate at the same speed / pace.
Hope this helps! Brainliest and / or a rating out of 5 stars would be appreciated :)
What is the value of m in the equation {m-ăn = 16, when n=8?
Find the slope of the line through the given points.
(6, 1) and (7,-2)
Answer:
slope -3
y-intercept 19
Step-by-step explanation:
Aaron is growing two tomato plants. At the last measurement, the first plant was 6.53 inches tall and the second was 2.7 inches tall.
How much taller was the larger plant?
3.83 inches
Answer:
3.83
Step-by-step explanation:
W 3 Aisha has $100 saved from her job. She wants to buy as many charms for her bracelet, at $4 each and earrings at $5 per set, as she can without spending all of her money. The inequality represents her spending, where x is the number of charms and y is the number of sets of earrings. 4x + 5y < 100
Simplifying 4x + 5y < 100 Solving 4x + 5 < 100. Solving for variable 'x' move all terms containing x to the left, all other terms to the right.
Hope i helped (❁´◡`❁)
Brainliest?
round 7, 525 to the nearest hundreds
Answer:
7,525 = 7,500
Step-by-step explanation:
Answer:
7,500
Step-by-step explanation:
2 Question help
5
A robot can complete 7 tasks in hour. Each task takes the same amount of time.
6
a. How long does it take the robot to complete one task?
b. How many tasks can the robot complete in one hour?
a. It takes the robot hour(s) to complete one task.
Step-by-step explanation:
60 divided by 7 = approx. 8-9 min for each task.
7 tasks per hour
Answer:
a. 8.58 (8.57142857143)
Step-by-step explanation:
Forty five percent of middle schools have a horse as a mascot. If there are 420 middle schools how many have a horse as a mascot ?