- #1

- 82

- 0

## Homework Statement

prove or refute:

if lim(a(2n)-a(n)=o , then a(n) is a cauchy sequence

## Homework Equations

## The Attempt at a Solution

I need to prove that for every m,n big enough a(m)-a(n)<epsilon

so I know for all m and n I can say m=l*n, lim(a(m)-a(n))=lim(a(n*l)-a(n*l/2) +a(n*l/2) -a(n*l/4)..........+a(2n)-a(n)), which is the sum of alot of zeros, though if I take m to be 2^n or something like that, I get an inifinite amount of zeros, so I don't know what I can do with that.

so I tried to find a sequence which contredicts it, though couldn't find any

## Homework Statement

prove or refute:

if |a(n+1)-a(n)|<9/10*|a(n)-a(n-1)|

then a(n) is a cauchy sequence

## Homework Equations

## The Attempt at a Solution

well fromt he equation I can get:

(|a(n+1)-a(n)|)/(|a(n)-a(n-1))<9/10<1

so what it gives me is that all that in the power of n is going to zero, which means is a cauchy sequence, thoguh I don't see how it helps me =\