Firstly, I think your equation to proove is wrong. I believe it should start:

Assuming that's right, we first need to proove it is true for n=1. A quick calculation is all that's required there - we find both sides are equal to

Now we say "Assuming the statement is true for n=k, will it be true for n=k+1?" What we are assuming is the following:

What we are trying to show is that

Now the RHS simplifies to

To proove, rewrite the LHS:

Now you just need to add the fractions, multiply out the numerator, re-factorise it and you should be there!