4 24+1 ( 6 pts. Find the sum of the series > - Express your result...
Express the series S = IM8 k 24 3k k= 1 as a power series by differentiating Ž *" Il for x| < 1. What is the value of S? 1- x n=0
Find a formula for the nth partial sum of the series and use it to find the series' sum if the series converges. 13 13 (n + 1)(n+2) What is the formula for the nth partial sum of the series? Sn=0 What is the sum of the series? Select the correct choice below and, if necessary, fill in the answer box to complete your answer. (Type an integer or a simplified fraction.) O A. The sum of the series is...
Euler found the sum of the p-series with p = 4: Use Euler's result to find the sum of the series Euler found the sum of the p-series with p = 4: 1 ga) = n4 90 n=1 Use Euler's result to find the sum of the series. 314 n=1 (k - 1)4 k=4
6. Short answer. (a) (2 pts) Find the sum of the series (-1)" =1-1-1-1+1-1+... or explain why it diverges. ( 5) (b) (2 pts) Find the sum of the series or explain why it diverges. n=0
Find a formula for the nth partial sum of the series and use it to determine if the series converges or diverges. If the series converges, find its sum. 10 Σ 10 n+1 n n=1 Sn If the series converges, what is its sum? Select the correct choice below and, if necessary, fill in the answer box to complete your choice. O A. The series sum is (Type an integer or a fraction.) B. The series diverges.
4. [5] Find a formula for the nth partial sum Sn of the series, as is done in Example 8 of chapter 11.2. Then, find the sum of the series or show that it diverges. Lk2 + 3k + 2 k=1
2. Find the sum of the serie 3-5*+1-6-24+2 -. Give your answer in exact form. 74
1 points Save An Find the exact sum of the following series ((-1)* (24/(2k!)) k=0 (Note: Write your answers as decimal numbers rounded to five decimal places, and make sure your calculator is in radian mode)
10) (4 pts.) If we approximate the sum of the series E 74+1 by adding the first 3 terms, what do we (-1)"n² know about how close the approximation is to the exact sum of the series? N-
0 31 -1 Determine whether the series converges or diverges. If it converges, find its sum. n =0 Select the correct choice below and, if necessary, fill in the answer box within your choice. 3h -1 = 0. The sum of the series is ОА. The series converges because lim . (Type an integer or a simplified fraction.) O B. The series diverges because it is the difference between two geometric series, at least one with Ir| 21. The series...