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Let {an}1 and {bn}n=1 be sequences. Prove or disprove: If {an – bn}=1 converges to 0 and {an}-1 converges to A, then {bn}=1 also converges to A.

Let {an}1 and {bn}n=1 be sequences. Prove or disprove: If {an – bn}=1 converges to 0 and {an}-1 converges to A, then {bn}=1 also converges to A.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Let \(\{a_n\}_{n=1}^\infty\) and \(\{b_n\}_{n=1}^\infty\) be sequences. Prove or disprove: If \(\{a_n - b_n\}_{n=1}^\infty\) converges to 0 and \(\{a_n\}_{n=1}^\infty\) converges to \(A\), then \(\{b_n\}_{n=1}^\infty\) also converges to \(A\).
Transcribed Image Text:Let \(\{a_n\}_{n=1}^\infty\) and \(\{b_n\}_{n=1}^\infty\) be sequences. Prove or disprove: If \(\{a_n - b_n\}_{n=1}^\infty\) converges to 0 and \(\{a_n\}_{n=1}^\infty\) converges to \(A\), then \(\{b_n\}_{n=1}^\infty\) also converges to \(A\).
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