Leibniz's Theorem (Alternating Series Test of Convergence) says $$\(\sum_{n=1}^{\infty},(-1)^{n+1}\)$$, and $$\(\frac{n+1}{n}\)$$ will converge because I. $$\(\frac{n+1}{n}\)$$ is positive. II. $$\(\frac{n+2}{n+1} \leq \frac{n+1}{n}\)$$. III. $$\(\lim _{n \rightarrow \infty} \frac{n+1}{n}=1\)$$.

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