• recategorized by
483 views
1 1 vote

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.

Please log in or register to answer this question.

Position:
Show:

Related questions

1 1 vote
0 0 answers
288
288 views
admin asked Dec 5, 2022
288 views
Let $\lim _{n \rightarrow \infty} x_{n}=x$. Then which of the following is $\text{TRUE.}$There exists an $n_{0}$, such that for all $n>n_{0},\left|x_{n}-x\right|=0$.There...
1 1 vote
0 0 answers
289
289 views
admin asked Dec 5, 2022
289 views
Let $f(x, y)$ be a function in two variables $x, y$. Then which of the following is true$\max _{x} \min _{y} f(x, y) \leq \min _{y} \max _{x} f(x, y)$.$\max _{x} \min _{y...
1 1 vote
0 0 answers
571
571 views
admin asked Dec 5, 2022
571 views
Let $f(x)=|x|$, for $x \in(-\infty, \infty)$. Then$f(x)$ is not continuous but differentiable.$f(x)$ is continuous and differentiable.$f(x)$ is continuous but not differe...
1 1 vote
0 0 answers
327
327 views
admin asked Dec 14, 2022
327 views
Evaluate the limit\[\lim _{n \rightarrow \infty}\left(2 n^{4}\right)^{\frac{1}{3 n}} .\]$e$$1$$2^{\frac{1}{3}}$$0$None of the above

Add Synced Question

×