consider-the-series-m11mm2m1displaystyle-summ1infty-frac-1m-m2m-1-does-this-seri

Question

Consider the series ∑m=1∞(−1)mm2m+1\displaystyle{ \sum_{m=1}^{\infty}} \frac{(-1)^m m}{2m + 1} . Does this series converge?

Accepted Answer

No, the series diverges

Answer

Yes, the series converges

Consider the series ∑m=1∞(−1)mm2m+1\(\displaystyle{ \sum_{m=1}\)^{\(\infty\)}} \(\frac{(-1)^m m}{2m + 1}\) . Does this series converge?