$a.\frac{1}{2}+\frac{1}{6}+\frac{1}{12}+...+$ $\frac{1}{100.101}$
= $\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+...+\frac{1}{100.101}$
= $\frac{1}{1}-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{100}-\frac{1}{101}$
= $\frac{1}{1}-\frac{1}{101}$
= $\frac{100}{101}$
b. $\frac{2}{15}+\frac{2}{35}+\frac{2}{63}+...+\frac{2}{323}$
= $\frac{2}{3.5}+\frac{2}{5.7}+\frac{2}{7.9}+...+\frac{2}{17.19}$
= $\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+\frac{1}{7}-\frac{1}{9}+...+\frac{1}{17}-\frac{1}{19}$
= $\frac{1}{3}-\frac{1}{19}$
= $\frac{16}{57}$
Chúc bạn học tốt !!!!!
