Hi, i've been solving some excersices but I am stuck with this one.

Proof by Mathematical Induction the following expresion

Well the first thing I did was rewrite the expesion as this:

then i proof this is true for p(1)

then I assume this true for p(k)

p(k+1)

then

replacing S_{k}

and then i did the sum

after this step I don't really know what to do for symplify the expression, so if can help it would be great and if i made a mistake in previous steps please make know. thanks