# Math Help - big equation

1. ## big equation

2. You can simplify the LHS by rationalizing the denominator (multiplying by the conjugate over the conjugate and using difference of perfect squares on the bottom to eliminate square roots).

$\frac{1}{\sqrt{n}+\sqrt{n+1}}=\frac{1}{\sqrt{n}+\s qrt{n+1}} \times \frac{\sqrt{n}-\sqrt{n+1}}{\sqrt{n}-\sqrt{n+1}}=\frac{\sqrt{n}-\sqrt{n+1}}{n-(n+1)}$

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

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

i.e.

$\frac{1}{\sqrt{4}+\sqrt{5}}=\sqrt{5}-\sqrt{4}$

See if you can use this to solve the problem

3. Originally Posted by hotgal24
What course is this for?

You could do this in Excel, or use DivideBy0's hint that this is a telescoping series.

RonL