Question

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?

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