I need some help with mathematical induction. It's driving me insane.

Use mathematical induction to prove that:

Basis step: Prove 1 exists in S.

n = 1 LHS =

RHS =

= 1/3

So 1 exists in S

Inductive step:

Assume k exists in S. We must prove k+1 exists in S

So assume

LHS =

RHS =

After this i just get lost, i think i have a problem when trying to perform arithmetic on it. Any help would be much appreciated.

I also have another question:

Find a fourth order polynomial with integer coefficients for which

is a root.

SO we have

any help would be much appreciated!