Question

Se dau nr.:

A: (1 - 1/2) * (1 - 1/3) * (1 - 1/4) * ... * (1 - 1/10)
B: (1 + 1/2) * (1 + 1/3) * (1 + 1/4) * ... * (1 + 1/10)

Dovediti ca: 2 * A * B = 11/20

Answer 1

A=(1 - 1/2) * (1 - 1/3) * (1 - 1/4) * ... * (1 - 1/10), aducem fiecare paranteza separat la acelasi numitor

=> A=1/2*2/3*3/4*……*9/10,  se simplifica si =>

A=1/10

B= (1 + 1/2) * (1 + 1/3) * (1 + 1/4) * ... * (1 + 1/10)

=> B=3/2*4/3*5/4*……*11/10, se simplifica

=> B=1/2*11/1

B=11/2

2*A*B=2*1/10*11/2=11/10