A Consider the following. (-5)k 4kk! k = 1 (a) Determine the smallest number of terms required to approximate the sum of the series with an error less than 0.0001. N = (b) Use a graphing utility to approximate the sum of the series with an error less than 0.0001. (Round your answer to four decimal places.)
A Consider the following. (-5)k 4kk! k = 1 (a) Determine the smallest number of terms required to approximate the sum of the series with an error less than 0.0001. N = (b) Use a graphing utility to approximate the sum of the series with an error less than 0.0001. (Round your answer to four decimal places.)
Chapter8: Sequences, Series,and Probability
Section8.1: Sequences And Series
Problem 9ECP: For the series i=1510i find (a) the fourth partial sum and (b) the sum. Notice in Example 9(b) that...
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Transcribed Image Text:A Consider the following.
(-5)k
4kk!
k = 1
(a) Determine the smallest number of terms required to approximate the sum of the series with an error less than 0.0001.
N =
n
(b) Use a graphing utility to approximate the sum of the series with an error less than 0.0001. (Round your answer to four decimal places.)
B
Find a value of n such that Sn approximates the series with an error of at most 10-5. If you have a CAS, compute this value
of Sn. (Round your answers to five decimal places.)
=
Sn =
k = 1
1.2(-1)k + 1 In k
k!
Test the series for convergence or divergence.
(−1)n + 1
3n4
n = 1
O converges
O diverges
If the series is convergent, use the Alternating Series Estimation Theorem to determine how many terms we need to add in
order to find the sum with an error less than 0.00005. (If the quantity diverges, enter DIVERGES.)
terms
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