> 
> Let $a\_n$ be q bounded sequence such that $$a\_n-a\_{n+1}\leq \frac{1}{2^n}$$
>  Let b\_n be a sequence such that $$b\_n=a\_n-\frac{1}{2^{n-1}}$$
> 
> 
> 

1. Prove that $a\_n$ converges.
2. Prove that $b\_n$ converges.

I think it's quite clear that if I prove (1), (2) will be immediate, from limit arithmetic.

I think I should solve this with Cauchy Sequences, I'm just not sure how.