Consider the equation

Define the sequence by

So that the sequence converges monotonically to the solution of the equation.

Proof so far.

I have and

So this sequence is monotonically increasing, but do I need to do induction to be more convincing?

I want to show that this sequence is bounded, so it does converge. Then suppose it converges to L. But I'm stuck here, guess I didn't start this right.

Any hints? Thanks.