Question

A convergent series from the given series is

• A. \[ \sum_{n=1}^{\infty}\frac{1}{\sqrt{n}} \]
• B. \[ \sum_{n=1}^{\infty}\frac{(-1)^n}{\sqrt{n+1}} \]
• C. \[ \sum_{n=1}^{\infty}\frac{3n^4+5}{n^2(n^2+4n+5)} \]
• D. \[ \sum_{n=3}^{\infty}\frac{\log n}{n} \]

Hint:

Remember: \[ \boxed{ \begin{aligned} \sum\frac1{n^p} &\text{ converges if }p>1, \sum(-1)^na_n &\text{ converges if }a_n\downarrow0. \end{aligned} } \]

Answer 1

The Correct Option is B