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Identitatea Botez-Catalan

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Una din formulările identităţii Botez-Catalan este:

1- \frac 1 2 + \frac 1 3 - \frac 1 4 + \cdots - \frac{1}{2n} = \frac{1}{n+1} + \frac{1}{n+2} + \cdots + \frac {1}{2n}, \; \forall n \ge 1. \!

O formulare echivalentă este următoarea:

\frac {1}{n+1} + \frac {1}{n+2} + \cdots + \frac{1}{2n+1} = 1- \frac 1 2 \left ( \frac {1}{1 \cdot 3} + \frac {1}{2 \cdot 5} + \cdots + \frac {1}{n(2n+1)} \right ), \; \forall n \ge 1. \!

Demonstraţia se face prin inducție matematică.

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