MathLiveSqueeze theorem
If a sequence is trapped between two sequences that both converge to the same limit L, then the trapped sequence also converges to L. It is used to find limits that are hard to compute directly by bounding them above and below.
\lim_{n\to\infty}a_n=\lim_{n\to\infty}c_n=L \land a_n\le b_n\le c_n \implies \lim_{n\to\infty}b_n=LWhat the symbols mean
| lower bounding sequence | |
| sequence trapped between the bounds | |
| upper bounding sequence | |
| common limit of the bounding sequences | |
| index of the sequence, tending to infinity |
About this formula
- FieldMathematics
- TopicLimits
- LevelHigh school
- Also calledpinching theorem, sandwich theorem, sandwich rule, squeeze lemma, limit sandwich theorem, squeeze theorem for sequences
- SourceWikidata Q1065257
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