Question

considerăm numerele raţionale: x = (1+1/2).(1+1/3)*(1+1/4)*...*(1+1/n) y= (1-1/2).(1-1/3)*(1-1/4)*...*(1-1/n), pentru n=5, calculati x*y

Answer 1

Aflam formula lui x:
x1: 1+1/2=3/2
x2: 1+1/3=4/3
x3: 1+1/4=5/4
.
.
xn=1+1/n=(n+1)/n
—————————(le inmultim)
se simplifica si ramane (n+1)/2
analog formula lui y: 1/n
n=5: (5+1)/2*1/2=6/2=3