Question

a) Pentru n€N , verificati daca (1-1/n)(1+1/n)=1-1/n la a doua
b) P =(1-1/2la a doua)(1-1/3 la a doua)(1-1/4 la a doua)......(1-1/100la a doua)

Answer 1

a)  (1 - 1/n)(1+1/n) = 1 - 1/n + 1/n - 1/n² = 1 - 1/n²
b) P = (1 - 1/2²)(1 - 1/3²)(1- 1/4²)............(1 - 1/100²)
P = (1-1/2)(1+1/2)(1-1/3)(1+1/3)(1-1/4)(1+1/4)............(1-1/100)(1+1/100)
P = 1/2·3/2·2/3·4/3·3/4·5/4·.......................99/100·101/100
P = 1/2 ·101/100 = 101/200