Question

Let an = $(1+\frac{1}{n})^{\frac{n}{2}}$ be the n𝑡ℎ term of the sequence 〈an 〉, n = 1, 2, 3, …. Then which one of the following is NOT CORRECT?

• A. ⟨an⟩ is bounded
• B. ⟨an⟩ is increasing
• C. $∑^∞ _{n=1}$ in (an) is a convergent series
• D. $lim\\\\_{n\rightarrow{∞}}(\frac{1}{n}∑^n_{k=1}a_k)=\sqrt{e}$

Answer 1

Answer: (C)

$∑^∞ _{n=1}$ in (an) is a convergent series

Answer 2

The correct option is (C): $∑^∞ _{n=1}$ in (an) is a convergent series