Question

Converge or Diverge (With justification).
Series from 1 to infinity of ((1+n)^.5-(n-1)^.5)/n

Answer 1

multiply top and bottom by \[\sqrt{1+n}+\sqrt{n-1}\]

Answer 2

then simplify...that should lead you in the right direction

Answer 3

2/n(1+n)^.5-(n-1)^.5)... so does that converge?

Answer 4

you get

\[\sum_{n=1}^{\infty}\frac{2}{n\left(\sqrt{1+n}+\sqrt{n-1}\right)}\]

Answer 5

I realize, but how do i justify if it converges or diverges?

Answer 6

use the limit comparison test

Answer 7

Thank you.