# Math Help - How do I prove sinh x?

1. ## How do I prove sinh x?

I need to prove the Maclarin Expansion of $Sinh (x)$.I know $Sinh (x) = (e^x - e^-x)/2$ but where do go from here? Please Help.

2. ## Sinh x

Hello rideorsmurf
Originally Posted by rideorsmurf
I need to prove the Maclarin Expansion of $Sinh (x)$.I know $Sinh (x) = (e^x - e^-x)/2$ but where do go from here? Please Help.
Use the expansions of $e^x$ and $e^{-x}$:

$e^x = 1 + x + \frac{x^2}{2!}+ \frac{x^3}{3!}+ \frac{x^4}{4!}+ \frac{x^5}{5!}+ \dots$

$e^{-x} = 1 - x + \frac{x^2}{2!}- \frac{x^3}{3!}+ \frac{x^4}{4!}- \frac{x^5}{5!}+ \dots$

... and subtract:

$e^x-e^{-x} = 2x +2\frac{x^3}{3!}+ 2\frac{x^5}{5!}+ \dots$

$\Rightarrow \sinh x =x +\frac{x^3}{3!}+ \frac{x^5}{5!}+ \dots$