# Applying Alternating Series Error(I think): Is there a typo in this question?

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 $n+1$?

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. $$\sum_{n=1}^\infty \frac{(-1)^{n+1}}{n^2 + 1}=-\sum_{n=1}^\infty \frac{(-1)^{n}}{n^2 + 1}$$
• $99$ terms sufficies. python code shows that the minimal required terms are fewer than that actually. Nov 23, 2017 at 2:31