Question

For p, q, r ∈ ℝ, r ≠ 0 and n ∈ $\N$, let
$a_n=p^n n^q(\frac{n}{n+2})^{n^2}$ and $b_n=\frac{n^n}{n!r^n}(\sqrt{\frac{n+2}{n}})$.
Then, which one of the following statements is TRUE ?

• A. If 1 < p < e2 and q > 1, then $\sum\limits_{n=1}^{\infin}a_n$ is convergent
• B. If e2 < p < e4 and q > 1, then $\sum\limits_{n=1}^{\infin}a_n$ is convergent
• C. If 1 < r < e, then $\sum\limits^{\infin}_{n=1}b_n$ is convergent
• D. If $\frac{1}{e}$ < r < e, then $\sum\limits^{\infin}_{n=1}b_n$ is convergent

Answer 1

Answer: (A)

If 1 < p < e2 and q > 1, then $\sum\limits_{n=1}^{\infin}a_n$ is convergent

Answer 2

The correct option is (A) : If 1 < p < e2 and q > 1, then $\sum\limits_{n=1}^{\infin}a_n$ is convergent.