- #1

jaqueh

- 57

- 0

## Homework Statement

Suppose the sequence (Sn) is defined as:

|S

_{n+1}-S

_{n}|<2

^{-n}

show that this is a cauchy sequence

## Homework Equations

hint: prove the polygon identity such that

d(Sn,Sm)≤d(Sn,Sn+1)+d(Sn+1,Sn+2)...+d(Sm-1,Sm)

## The Attempt at a Solution

I have defined Sm and Sn and created the inequality that:

d(S

_{n},S

_{m})=|2

^{-n}-2

^{-m}|>||S

_{n+1}-S

_{n}|-|S

_{m+1}-S

_{m}||