**TI82** TxtView file generated by CalcText - Kouri¦ —ROC Bern—•ÿROC BernoulliROC Bernoulli Soit un nbr reel a>0 Dem que pr tt ent nat n, on a: (1+a)^n>=1+na pr tt n>=0 Ini: (1+a)^0=1 car 1+a>=1>0 dc 1+a=/0 1+a0=1 Dc (1+a)^0>=1+0a Her: Sup pr un rg k>=0: (1+a)^k>=1+ka On a (1+a)^k>=1+ka (1+a)^k(1+a)>=(1+ka)(1+a) car a>0 dc 1+a>1>0 On a dc (1+a)^(k+1)>=1+ka+a+ka^2 (1+a)^(k+1)>=1+(k+1)a+ka^2 Ccl: Pr tt reel a>0, on a pr tt ent nat n: (1+a)^n>=1+naÿƒp