Question

Tính 1/1.2.3 + 1/2.3.4 + ... + 1/49.50.51

Answer 1

\(\frac{1}{1.2.3}+\frac{1}{2.3.4}+...+\frac{1}{49.50.51}\)

= \(\frac{2}{1.2.3}+\frac{2}{2.3.4}+...+\frac{2}{49.50.51}\)

= \(\frac{2-1}{1.2.3}+\frac{4-2}{2.3.4}+...+\frac{51-49}{49.50.51}\)

= \(\frac{1}{1.3}-\frac{1}{2.3}+\frac{1}{2.3}-\frac{1}{3.4}+...+\frac{1}{49.50}-\frac{1}{50.51}\)

= \(\frac{1}{3}-\frac{1}{50.51}\)

= \(\frac{1}{3}-\frac{1}{2550}\)

= \(\frac{283}{850}\)