Réponses

2013-10-12T21:49:14+02:00
U_{n+1} - U_{n} = ((1/n+1) + (1/n+2) + ......+ (1/2n+2)) - ((1/n) + (1/n+1) + ...... (1/2n)) = (1/2n+1) + (1/2n+2) - (1/n) =  \frac{2n+2+2n+1}{(2n+1)(2n+2)} - \frac{1}{n}  \frac{4n+3}{(2n+1)(2n+2)} - \frac{1}{n}  \frac{-3n - 2}{n(2n+1)(2n+2)}