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Approximate the value of the series to within an error of at most 10−510−5. ∑n=1[infinity](−1)n+1n7 ∑n=1[infinity](−1)n+1n7 According to Equation (2): |SN−S|≤aN+1 |SN−S|≤aN+1 what is the smallest value of NN that approximates SS to within an error of at most 10−510−5?

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sakhilemdletshesm

Answer:

0.992596

Step-by-step explanation:

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If value of the series to within an error is 10^−5. The smallest value of N that approximates S to within an error of at most 10^−5 is: 0.99259.

Smallest value of N

First step is to find the term n that will satisfy the condition

(αn+1)<10^-5

(-1)^n+1÷(n+1)^7<10^-5

=1÷(n+1)^7<10^-5

=(n+1)^7>10^-5

=n>10^5/7-1

=n>4.179

Second step is to expand the series up to 5 terms in order to find the smallest value

∑ (-1)^n+1÷n^7=(-1)^1+1÷1^7+=(-1)^2+1÷2^7+=(-1)^3+1÷3^7+=(-1)^4+1÷4^7+=(-1)^5+1÷5^7

=1+(-1÷128)+(1÷2187)+(-1÷16384)+(1÷78125)

=0.99259

Therefore the smallest value of N that approximates S to within an error of at most 10^−5 is 0.99259.

Learn more about smallest value of N here:https://brainly.com/question/2881645

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