Determine if the series converges or diverges. If the series converges, find its sum. 5) sum_{n=1}^{infty} left( frac{1}{sqrt{n+1}} - frac{1}{sqrt{n+3}} ight) A) converges; frac{1}{sqrt{3}} + frac{1}{2} B) converges; frac{1}{sqrt{3}} + frac{1}{sqrt{6}} C) converges; frac{1}{sqrt{2}} + frac{1}{sqrt{3}} D) diverges
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To determine if the series converges or diverges, we can use the nth term test. This test states that if the limit of the nth term as n approaches infinity is not zero, then the series diverges. If the limit is zero, then the test is inconclusive and we need to Show more…
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