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

The Correct Option is C

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