need help with two questions:

prove with inducation that for every natural n exists:

$\displaystyle \frac{1}{(1+a)^n}+\frac{1}{(1-a)^n}\geq2$

(-1<a<1)

the second:

$\displaystyle \frac{2}{(a+b)^n}<\frac{1}{a^n}+\frac{1}{b^n}$

(a>0, b>0)

many thanks