What would you say about this series about convergence and absolute convergence?
$$\sum_{n=0}^\infty \left (\frac{(-1)^n}{n+1}+\frac{(-1)^{n+1}}{n+2} \right )$$
In use with: $$\sum_{n=1}^∞ \frac{1}{n^2}$$
2026-03-26 14:23:04.1774534984
Convergence of $\sum_{n=0}^\infty \left (\frac{(-1)^n}{n+1}+\frac{(-1)^{n+1}}{n+2} \right )$
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$$\sum_{n=0}^\infty \left(\frac{(-1)^n}{n+1}+\frac{(-1)^{n+1}}{n+2}\right)=\sum_{n=0}^\infty \left(\frac{(-1)^n}{n+1}-\frac{(-1)^{n}}{n+2}\right)=\sum_{n=0}^∞ \frac{(-1)^n}{(n+1)(n+2)}$$ then compare with $\frac{1}{n^2}$