Ta có:
A=(1+$\frac{1}{2}$)(1+$\frac{1}{3}$)(1+$\frac{1}{4}$)......(1+$\frac{1}{99}$)
=($\frac{2}{2}$+$\frac{1}{2}$)($\frac{3}{3}$+$\frac{1}{3}$)($\frac{4}{4}$+$\frac{1}{4}$)+......+( $\frac{99}{99}$+$\frac{1}{99}$)
= $\frac{3}{2}$.$\frac{4}{3}$.$\frac{5}{4}$..........$\frac{100}{99}$
=$\frac{3.4.5.....100}{2.3.4.....99}$
= $\frac{100}{2}$=50
B=$\frac{3}{4}$.$\frac{8}{9}$.$\frac{15}{16}$.......$\frac{899}{900}$
=$\frac{1.3}{2.2}$.$\frac{2.4}{3.3}$.$\frac{3.5}{4.4}$.....$\frac{29.31}{30.30}$
= $\frac{1.2.3.....29}{2.3.4.....30}$.$\frac{3.4.5.....31}{2.3.4.....30}$
= $\frac{1}{30}$.$\frac{31}{2}$=$\frac{31}{60}$
Chúc học tốt!!!
