Question

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

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

Answer 1

The Correct Option is C

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