Hi I am having a bit of trouble expressing the answer to a problem. If it is any constellation this problem goes alongside convergence proofs.

be sequences such that and if n is even

or if n is odd. Show that

That being said if n is even . As is a subsequense of one can conclude that converges to . Hence will converge to a if n is even.

As is a is a constant. will also converge to .

As converges to a in both cases, then as stated.

I think this is the idea behind the question, if I overlooked anything please tell me. Thank you. (Happy)