Hi I am having a bit of trouble with a couple of questions in regards to convergences.

Let the sequence

let

Prove that

Hence prove that

From my attempts at part 1 I have been able to show that for n=0 and n=1 that the function will be equal to and respectively. However I am having trouble actually proving for n terms that it is true. I am able to get to but am completely stuck there on.

For the second part I have very little idea as to how I can prove that the sequence converges using my result from part 1.

Thanks you for any input in advance :d