Define a sequence, and

Prove that

Proof by induction

When n=1, it is true

Assume true for n=k

Test n=k+1

By hypothesis, this is true for the numerators, now testing the denominators

if

it is always true

Simplifying

However, this is not always true.

Now I need help. I am unsure how to proceed, or any of the preceding steps are wrong and I need to find a new method t solve the problem.

All help greatly appreciated