Exercise · ZW-UNIQUENESS-OF-LIMITS-004 · ★☆☆ Basic
In the proof, \(N_1\) works for convergence to \(L\) and \(N_2\) for convergence to \(M\). If \(N_1=12\) and \(N_2=30\), which index works for both at once?
Choose one option.
Show answer
- D. \(30\)
Explanation
We need \(n\ge N_1\) and \(n\ge N_2\); \(N=\max(12,30)=30\) is enough.
Review the concept: Uniqueness of limits
Uniqueness of limits says that a sequence \((a_n)\) cannot converge to two different numbers \(L\) and \(M\); that is why it makes sense to speak of “the” limit.
\[a_n\to L,\ a_n\to M\ \Rightarrow\ L=M\]
More practice problems: uniqueness of limits
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