Find the minimum number of terms needed to approximate the series ... correct to 1DP

Question

The series is $\sum_{k=1}^{\infty}\frac{(-1)^{k+1}k}{k^2+1}$

The minimum number of terms needed should be given by $\lvert a_{n+1} \rvert$

Thus $\lvert \frac{(-1)^{k+2}(k+1)}{(k+1)^2+1} \rvert<0.01$

However, this is only satisfied after the $99th$ term, whereas the answer says the $19th$ term.

Answer 1

For 1dp the bound should be.05, not .01.