indeed. as i said javax, induction is the way i usually see this done. and you are to show the sequence is monotonic and bounded, because then, a theorem tells us it converges (by the way, it is in proving the limit exist that you realize which of the answers in the second part to disregard)

yes. so when we take the limit, all the

's go to

, and we get the expression i have there

now we must solve for

. begin by expanding the right hand side, and then try to get all the

's on one side to solve for