
Originally Posted by
icelated
I am trying to confirm the integral test can be applied. I just cant see how the solution manual gets there solution.
I think there using the quotient rule but i cant seem to work it out.
Can someone help me work out the problem?
$\displaystyle \sum_{n=1}^\infty \frac 1 {\sqrt {n} ( \sqrt {n} + 1 )} $
then,
Let $\displaystyle f(x) = \frac 1 {\sqrt {x} ( \sqrt {x} + 1 )} $
The solution manual then shows!
$\displaystyle f'(x) = \frac {1+2\sqrt x} { 2x^{3/2} ( \sqrt x + 1 )^2} < 0$
With the denominator squared it does show they use the quotient rule. However, can you please
show me the steps on how they derive the answer?
Because i cant seem to get it. Its kinda a nasty problem.
Thank you so very much!