Alright, so here's the first problem.

Prove that for all positive integers n, .

This is what I have so far;

For n=1,

Assume this is true for some . Now, for n+1,

That last part is where it is hazy.

Other problem I was having trouble with is,

Show for positive integers n,

.

I have a lot of crazy things for this so far. I think this, " " is the beginning of the way to take it, but I'm not sure.

Any help or new direction is greatly appreciated. Thanks a bunch in advance!