A=(1+$\frac{1}{2}$) . (1+$\frac{1}{3}$) .(1+$\frac{1}{4}$) ...(1+$\frac{1}{99}$ )
=($\frac{2}{2}$ +$\frac{1}{2}$)).($\frac{3}{3}$+$\frac{1}{3}$)......($\frac{99}{99}$+$\frac{1}{99}$)
=$\frac{3}{2}$.$\frac{4}{3}$.$\frac{5}{4}$............$\frac{100}{99}$
=$\frac{3.4.5....100}{2.3.4...99}$
= $\frac{100}{2}$ (sau khi rút gọn cả tử lẫn mẫu:3.4.5...99)
= 50