cmi-entrance 2020 Q6

cmi-entrance · India · pgmath 4 marks Not Maths Convergence/Divergence Determination of Numerical Series
Which of the following is/are true for a series of real numbers $\sum a_{n}$?
(A) If $\sum a_{n}$ converges then $\sum a_{n}^{2}$ converges;
(B) If $\sum a_{n}^{2}$ converges then $\sum a_{n}$ converges;
(C) if $\sum a_{n}^{2}$ converges then $\sum \frac{1}{n} a_{n}$ converges;
(D) If $\sum |a_{n}|$ converges then $\sum \frac{1}{n} a_{n}$ converges;
Which of the following is/are true for a series of real numbers $\sum a_{n}$?\\
(A) If $\sum a_{n}$ converges then $\sum a_{n}^{2}$ converges;\\
(B) If $\sum a_{n}^{2}$ converges then $\sum a_{n}$ converges;\\
(C) if $\sum a_{n}^{2}$ converges then $\sum \frac{1}{n} a_{n}$ converges;\\
(D) If $\sum |a_{n}|$ converges then $\sum \frac{1}{n} a_{n}$ converges;