Use the alternating series estimation theorem to determine how many terms should be used to estimate the sum of the entire series with an error of less than 0.001 or more terms should be used to estimate the sum of the entire series with an error of less than 0.001. sum^infty_n=1 (-1)^n 1/n^2+5

umthumaL3e

umthumaL3e

Answered question

2022-11-26

Use the alternating series estimation theorem to determine how many terms should be used to estimate the sum of the entire series with an error of less than 0.001 or more terms should be used to estimate the sum of the entire series with an error of less than 0.001.
n = 1 ( 1 ) n 1 n 2 + 5

Answer & Explanation

Kael Gill

Kael Gill

Beginner2022-11-27Added 8 answers

n = 1 ( 1 ) n 1 n 2 + 5 a n = 1 n 2 + 5 | R n | a n + 1 a n + 1 0.001 1 ( n + 1 ) 2 + 5 0.001 1 n 2 + 1 2 + 2 n + 5 1 10 3 n 2 + 2 n + 6 10 3 n 2 + 2 n 994 0
So, true for n 31

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