Show :$\displaystyle (\frac{1}{1*3})+ (\frac{1}{2*4})+ (\frac{1}{3*5})+.....=\frac{3}{4}$

When i do the problem i keep getting $\displaystyle \frac{3}{2}$instead of [tex]\frac{3}{4}/MATH]

Heres how im doing it

$\displaystyle (1-\frac{1}{3})+(\frac{1}{2}-\frac{1}{4})+(\frac{1}{3}-\frac{1}{5})+...$

which gives me as the lim n appraoches infinity $\displaystyle (\frac{3}{2}-\frac{1}{n+2})$

I dont see where i am going wrong or how to get $\displaystyle \frac{3}{4}$