Approximate the value of the series to within an error of at most 10-5. ∑n=1[infinity] (-1) n+1n6 According to Equation (2) : |SN-S|≤aN+1 what is the smallest value of N that approximates S to within an error of at most 10-5?

Question

Mathematics

Cannon Klein

16 September, 15:47

Approximate the value of the series to within an error of at most 10-5. ∑n=1[infinity] (-1) n+1n6 According to Equation (2) : |SN-S|≤aN+1 what is the smallest value of N that approximates S to within an error of at most 10-5?

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Answers (1)

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Daniel Rose · Answer 1

Answer:1 / (N+10) (N+7) ≤10-3

Step-by-step explanation:

S=∑∞n=1 (-1) ^n+1 / (n+9) (n+6)

|SN-S|≤aN+1|SN-S|≤aN+1,

SN=∑Nn=1 (-1) ^n+1 / (n+9) (n+6)

|an+1|≤|an|

limn→∞ an=0

|SN-S|≤aN+1

aN+1=1 ((N+1) + 9) ((N+1) + 6)

1 / (N+10) (N+7) ≤10-3