Order Midpoint method

Source: Wikipedia:
Runge?Kutta methods - Wikipedia, the free encyclopedia

An example of a second-order method with two stages is provided by the midpoint method

$\displaystyle y_{n+1} = y_n + hf\left(t_n+\frac{h}{2},y_n+\frac{h}{2}f(t_n, y_n)\right). $

I want to show that the midpoint method is a second-order mathod. But I dont know how to do that.

I guess I have to find Taylor series

Does anyone have any idea how to do this? Any help would be greatly appreciated!