Question

\[n\in \mathbb{N}\]
Show that :
\[\frac{1}{\sqrt{n}}-\frac{1}{\sqrt{n+1}}=\frac{1}{n\sqrt{n+1}+(n+1)\sqrt{n}}\]
Tipp: expand with \[(\frac{\sqrt{n+1}+\sqrt{n}}{\sqrt{n+1}+\sqrt{n}})\]

Answer 1

hint : use the given tip

Answer 2

multiply the left hand side by the given special kind of 1

Answer 3

Hey Ganeshie, i tried already but i couldnt come to solution