Question

Se considera functia f:R-{-1}->R, f(x)=x/x+1. Calculati produsul : P=f(1)*f(2)*...f(100)

Answer 1

P=$\frac{1}{2} \frac{2}{3} \frac{3}{4} \frac{4}{5} \frac{5}{6} \frac{6}{7} ... \frac{100}{101} = \frac{1}{101}$
Se observa ca se simplifica toti termenii mai putin 101

Answer 2

P=1/2 * 2/3*3/4*....*99/100*100/101= 1/101
as simple as that!!!