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.
- ted sLv 72 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