Prove that:

My work so far:

Let P(n) denote the statement that

The statement holds true for the case n = 1.

Assume that P(n) is true for when n is equal to a natural constant k,

Prove that P(n) is true when n = k + 1

Replacing the terms on the left hand side of P(k+1) with the right hand side of P(k) I then had:

This is as far as I could get! I need assistance simplifying the left hand side of this last line, assuming I have worked this through correctly. I have not worked too much with sequences so my trouble is mainly with getting a common denominator. Thanks for anyone that helps with this, I know it is a lot to read through.