Question

Suppose $a_n = \frac{3^n + 3}{5^n - 5} \quad \text{and} \quad b_n = \frac{1}{(1 + n^2)^{1/4}} \quad \text{for} \ n = 2, 3, 4, \ldots$ Then which one of the following is true?

• A. Both $\sum_{n=2}^\infty a_n$ and $\sum_{n=2}^\infty b_n$ are convergent.
• B. Both $\sum_{n=2}^\infty a_n$ and $\sum_{n=2}^\infty b_n$ are divergent.
• C. $\sum_{n=2}^\infty a_n$ is convergent and $\sum_{n=2}^\infty b_n$ is divergent.
• D. $\sum_{n=2}^\infty a_n$ is divergent and $\sum_{n=2}^\infty b_n$ is convergent.

Answer 1

Answer: (C)

$\sum_{n=2}^\infty a_n$ is convergent and $\sum_{n=2}^\infty b_n$ is divergent.

Answer 2

The correct option is (C): $\sum_{n=2}^\infty a_n$ is convergent and $\sum_{n=2}^\infty b_n$ is divergent.