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GATE2014-28

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Which of the following statements is true for the series given below?

$$S_n=1+\frac{1}{\sqrt{2}}+\frac{1}{\sqrt{3}}+\frac{1}{\sqrt{4}}+\dots+\frac{1}{\sqrt{n}} $$

  1. $S_n$ converges to $\log(\sqrt{n})$
  2. $S_n$ converges to $\sqrt{n}$
  3. $S_n$ converges to $\exp(\sqrt{n})$
  4. $S_n$ diverges

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