Help with induction question

Question

I'm trying to prove the following equation by induction, but my base case isn't working.

for all n>2.

For my base case I did n=3, and on the LHS I got 8/9 and the RHS I got 2/3.

Helppp.

Answer 1

The left hand side is

$$\left(1-\frac{1}{2^2}\right)\left(1-\frac{1}{3^2}\right)=\frac{3}{4}\frac{8}{9} = \frac23$$

and so is the right hand side:

$$\frac{3 + 1}{2\cdot 3} = \frac46=\frac23$$