Does it converge?

Calculus Level 3

$\large \frac{1}{1+\sqrt 1} + \frac{1}{1+\sqrt 2} + \frac{1}{1+ \sqrt 3} + \frac{1}{1+\sqrt 4} + \cdots$

Does the sum above converge?

Diverges Cannot be determined Converges

1 solution

Chew-Seong Cheong
Apr 10, 2017

Relevant wiki: Convergence - Comparison Test

Note that $\displaystyle \sum_{n=1}^\infty \frac 1{1+\sqrt n} > \sum_{n=1}^\infty \frac 1{2\sqrt n} > \sum_{n=1}^\infty \frac 1n$ . Since $\displaystyle \sum_{n=1}^\infty \frac 1n$ diverges, $\displaystyle \sum_{n=1}^\infty \frac 1{1+\sqrt n}$ diverges .

Does it converge?

1 solution

0 pending reports