Question

1 1/2*1 1/3*1 1/4*...1 1/100

Answer 1

Folosim faptul ca:
$1 \frac{1}{2} =1+\frac{1}{2}=\frac{2}{2}+\frac{1}{2}=\frac{3}{2}$
1 \frac{1}{3} =1+\frac{1}{3}=\frac{3}{3}+\frac{1}{3}=\frac{4}{3}
.............
1 \frac{1}{100} =1+\frac{1}{100}=\frac{100}{100}+\frac{1}{100}=\frac{101}{100}
Inmultind membru cu membru, obtinem:
Produsul initial=$\frac{3}{2} * \frac{4}{3} * \frac{5}{4} *...* \frac{101}{100} =$
si observam ca se reduc factori de la numarator cu factori de la numitor, iar in final ramane rezultatul=101/2