cmi-entrance 2014 Q8

cmi-entrance · India · pgmath 4 marks Not Maths
Which of the following statement(s) is/are true?
(A) The series $\sum_{n=1}^{\infty} \mathrm{e}^{-n^2}$ converges.
(B) The series $\sum_{n=1}^{\infty} \frac{(-1)^n}{n}$ converges.
(C) The series $\sum_{n=1}^{\infty} \frac{(-1)^n}{n}$ converges absolutely.
(D) The series $\sum_{n=1}^{\infty} \frac{\sin(nx)}{n^2}$ converges uniformly on $\mathbb{R}$.
Which of the following statement(s) is/are true?\\
(A) The series $\sum_{n=1}^{\infty} \mathrm{e}^{-n^2}$ converges.\\
(B) The series $\sum_{n=1}^{\infty} \frac{(-1)^n}{n}$ converges.\\
(C) The series $\sum_{n=1}^{\infty} \frac{(-1)^n}{n}$ converges absolutely.\\
(D) The series $\sum_{n=1}^{\infty} \frac{\sin(nx)}{n^2}$ converges uniformly on $\mathbb{R}$.