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