# Thread: algebraic fraction problem real one

1. ## algebraic fraction problem real one

Sum the series:

a1 + a2 + .... + a99

where an =
1
__________________________
(n+1)sqrt(n)+nsqrt(n+1)

For n = 1,2,...99

BTW THE LETTERS/NUMBERS ON RED ARE MEANT TO BE IN SUBSCRIPT
the sqrt in blue represents a square root sign for whatever follows it in brackets

2. $\frac{1}{(n+1)\sqrt{n}+n\sqrt{n+1}}=\frac{1}{\sqrt {n}\sqrt{n+1}(\sqrt{n+1}+\sqrt{n})}=$

$=\frac{\sqrt{n+1}-\sqrt{n}}{\sqrt{n}\sqrt{n+1}}=\frac{1}{\sqrt{n}}-\frac{1}{\sqrt{n+1}}$

Now, replace n with 1, 2, 3,....,99.