Question

Which of the following statements are correct:
A. If $\sum a_n$ converges, then $\lim_{n \to \infty} a_n = 0$ B. If $|a_n| \le c_n$ for all $n$, and if $\sum c_n$ diverges, then $\sum a_n$ diverges.
C. If $|a_n| \le c_n$ for $n \ge N_0$, ($N_0$ is fixed integer) and if $\sum c_n$ converges, then $\sum a_n$ converges.
D. If $a_n \ge d_n \ge 0$ for $n$, and if $\sum d_n$ converges, then $\sum a_n$ converges.
E. If $a_n \ge d_n \ge 0$ for $n \ge N_0$ and if $\sum d_n$ diverges, then $\sum a_n$ diverges.
Choose the correct answer from the options given below:

• A. A, B, D Only
• B. A, B, E Only
• C. A, C, E Only
• D. A, C, D Only

Hint:

Remember the Comparison Test direction: - Bigger series converges $\implies$ Smaller series converges. - Smaller series diverges $\implies$ Bigger series diverges.

Answer 1

The Correct Option is C