Find the number of terms required to determine the sum of the series with error less than .0001

$$\sum_{n=1}^\infty \frac{(-1)^\bbox[yellow]2}{n^2 + 1}$$

This problem appears in the section where I applied Alt. Series test on everything and I can assume that there is a typo in that the exponent of the numerator should be $n$ or $n+1$?


1 Answer 1


Most likely there is a typo as it makes no sense to write $(-1)^2$.

If you know the correction is either $n$ or $n+1$, either should give you the same answer since they only differ by a sign. $$\sum_{n=1}^\infty \frac{(-1)^{n+1}}{n^2 + 1}=-\sum_{n=1}^\infty \frac{(-1)^{n}}{n^2 + 1}$$

  • $\begingroup$ Is the answer 99 terms because the 100th term is less than .0001? $\endgroup$
    – Smit Shah
    Nov 23, 2017 at 2:11
  • $\begingroup$ $99$ terms sufficies. python code shows that the minimal required terms are fewer than that actually. $\endgroup$ Nov 23, 2017 at 2:31

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