Réponses

2013-11-23T18:59:48+01:00
Exercice 2
1) 2^1 se lit 2 puissance 1
2^1+2^1 = 2+2 = 4 = 2^2
2^2+2^2 = 4+4 = 8 = 2*2^2 = 2^3
2^3+2^3 = 8+8 = 16 = 2*2^3 = 2^4
2^4+2^4 = 16+16 = 32 = 2*2^4 = 2^5
2^-1 +2^-1 = 0.5+0.5 = 1 = 2^0
2^-2+2^-2 = 0.25+0.25 = 0.5 = 2^-1

2) Si n est un entier il semble que 2^n + 2^n = 2^(n+1)
Démonstration
2^n + 2^n = 1*2^n + 1*2^n = (1+1)2^n = 2*2^n = 2^1*2^n = 2^(n+1)

3) 3^n +3^n = 1*3^n + 1*3^n = (1+1)3^n = 2*3^n différent de  3^(n+1)