Question

Let x(n) a sequence , n E (N) for which there is an a>1 that |x(n+1)- x(n)| ≤ M a^{-n} , for every n E (N).
Prove that limx(n) = x , for a x that belongs to R.

Answer 1

hint: show that it is a Cauchy sequence

Answer 2

yeah i realize that it is suggesting that ithis sequence is a cauchy sequence but how do i show that?

Answer 3

then it has a converge sub sequence
and it is your answer

Answer 4

Care to explain it thoroughly?

Answer 5

awesome thanks!

Answer 6

I hope my hand write is useful
!