[Steps Shown] By considering the partial sums, prove directly that the series ∑_n=1^∞((1)/(√n)-(1)/(√n+1))
Question: By considering the partial sums, prove directly that the series
\[\sum_{n=1}^{\infty}\left(\frac{1}{\sqrt{n}}-\frac{1}{\sqrt{n+1}}\right)\]converges.
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