I think the solution I've found makes sense, but I'd like it to be double-checked.(adsbygoogle = window.adsbygoogle || []).push({});

1. The problem statement, all variables and given/known data

Let ##(a_n)## be a limited sequence and ##(b_n)## such that ##0≤b_n≤ \frac{1}{2} B_{n-1} ##

Prove that if

##a_{n+1} \ge a_{n} -b_{n}##

Then

##\lim_{n\to \infty}a_n##

exists.

3. The attempt at a solution

I can say that ##b_n \ge (\frac{1}{2})^n b_0 ## which is constant.

THen,

##a_n-a_{n+1} \ge (\frac{1}{2})^nb_0##

Thus ##|a_n-a{n+1}| ## is a Cauchy sequence, which means it converges and therefore the limit exists.

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# Homework Help: Convergence of a sequence

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