Infinite Seriesmedium
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Use rationalization to evaluate the telescoping series n=1(n+1n)\sum_{n=1}^{\infty} (\sqrt{n+1} - \sqrt{n}). Rationalize the numerator by multiplying by n+1+nn+1+n\frac{\sqrt{n+1}+\sqrt{n}}{\sqrt{n+1}+\sqrt{n}}.