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Aratati ca [tex] \frac{1}{n} - \frac{1}{n+1} = \frac{1}{n*(n+1)} ,pentru orice n[/tex] ∈ N*

Răspuns :

 [tex]\frac{1}{n}^{(n+1)} - \frac{1}{n+1}^{(n}= \frac{n+1-n}{n(n+1)}= \frac{1}{n(n+1)} \ (c.c.t.d)[/tex]