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8 June, 21:18

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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  1. 8 June, 21:36
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    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
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