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Convergence Induction for Positive Sequences: Proving Limit Behavior
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- mathmajo
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- Forum: Calculus and Beyond Homework Help
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Convergence Induction for Positive Sequences: Proving Limit Behavior
Homework Statement If (an) — > 0 and \bn - b\ < an, then show that (bn) — > b Homework Equations The Attempt at a Solution- mathmajo
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- Convergence Induction
- Replies: 3
- Forum: Calculus and Beyond Homework Help