dydx
Lv 6
dydx asked in Science & MathematicsMathematics · 8 months ago

Find the sum of the series.....?

Find the sum of the series

Σ(n = 1 to n = ♾) of ((-1)^(n+1)) / (n^5)

to four decimal places.

I'm a bit puzzled as to the procedure. Do I use the Alternating Series Estimation Theorem, or Taylor's Inequality? The book couldn't be more confusing as to what you are supposed to do regarding Taylor's Inequality, so I try to avoid it.

As for my answer, I got 0.9721 from the first 6 terms to get accuracy to within 4 decimal places.

1 Answer

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  • ted s
    Lv 7
    8 months ago

    | error after k terms | <  a_(k+1)......thus find k so that 1 / ( k+1)^5 < 10^(-5) ====> 10^5 < (k + 1) ^5 ===> k = 9...thus sum the 1st nine terms....do the work

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