(5 points) Determine whether the series $\sum_{k=1}^{\infty} (\sqrt{n+4} - \sqrt{n+3})$ converges or diverges. If the series converges, state where the series converges to.
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We can rewrite $a_n$ by multiplying the numerator and denominator by the conjugate: $$a_n = (\sqrt{n+4} - \sqrt{n+3}) \cdot \frac{\sqrt{n+4} + \sqrt{n+3}}{\sqrt{n+4} + \sqrt{n+3}} = \frac{(n+4) - (n+3)}{\sqrt{n+4} + \sqrt{n+3}} = \frac{1}{\sqrt{n+4} + Show more…
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