Convergence Induction for Positive Sequences: Proving Limit Behavior

[mathmajo]

Homework Statement

If (an) — > 0 and \bn - b\ < an, then show that (bn) — > b

Homework Equations

The Attempt at a Solution

 

[dirk_mec1]

Please show your attempt at the solution.

 

[mathmajo]

Since an --> 0, given some epsilon>0, there exists and m>0 such that /an-0/=/an/<epsilon for all n>m
thus, /bn-b/</an/<epsilon for all n>m
therefore, by definition bn-->b

 

[Dick]

Since an --> 0, given some epsilon>0, there exists and m>0 such that /an-0/=/an/<epsilon for all n>m
thus, /bn-b/</an/<epsilon for all n>m
therefore, by definition bn-->b

Looks ok to me.