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If $a_k$ is an increasing function of $k$, i.e. $a_1<a_2<\ldots<a_k \ldots$. Then which of the following is $\text{TRUE.}$

  1. $\lim _{n \rightarrow \infty} \sum_{k=1}^{n} \frac{1}{a_{k}}=\infty$.
  2. $\lim _{n \rightarrow \infty} \sum_{k=1}^{n} \frac{1}{\left|a_{k}\right|}<\infty$.
  3. Either $(a)$ or $(b)$.
  4. $\lim _{n \rightarrow \infty} \sum_{k=1}^{n} \frac{1}{a_{k}}=0$.
  5. None of the above.
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