edited by
138 views
0 votes
0 votes

Let $\left \{ a_{n} \right \}_{n=1}^{\infty }$ and $\left \{ b_{n} \right \}_{n=1}^{\infty }$ be two sequences of real numbers such that the series $\sum _{n=1}^{\infty }a_{n}^{2}$ and $\sum _{n=1}^{\infty }b_{n}^{2}$converge. Then the series $\sum _{n=1}^{\infty }a_{n}b_{n}$

  1. is absolutely convergent
  2. may not  converge
  3. is always convergent, but may not converge absolutely
  4. converges to $0$
edited by

Please log in or register to answer this question.

Answer:

Related questions

0 votes
0 votes
0 answers
1
soujanyareddy13 asked Aug 30, 2020
245 views
The value of the product $\left ( 1+\frac{1}{1!} +\frac{1}{2!}+\cdots \right )\left ( 1-\frac{1}{1!} +\frac{1}{2!}-\frac{1}{3!}+\cdots \right )$ is $1$$e^{2}$$0$$log_{e} ...
0 votes
0 votes
0 answers
2
soujanyareddy13 asked Aug 30, 2020
170 views
The value of the series $\sum _{n=1}^{\infty }\frac{n}{2^{n}}$ is$1$$2$$3$$4$.
0 votes
0 votes
0 answers
3