Question

Tính A=\(\frac{1}{2}+\frac{1}{6}+\frac{1}{12}+\frac{1}{20}+.....+\frac{1}{3×80}\)

Answer 1

A=\(\frac{1}{2}+\frac{1}{6}+\frac{1}{12}+\frac{1}{20}+.....+\frac{1}{3.80}\)

A=\(\frac{1}{2}+\frac{1}{6}+\frac{1}{12}+\frac{1}{20}+.....+\frac{1}{240}\)

A=\(\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+\frac{1}{4.5}+.....+\frac{1}{15.16}\)

A=\(1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+.....+\frac{1}{15}-\frac{1}{16}\)

A=\(1-\frac{1}{16}=\frac{16-1}{16}=\frac{15}{16}\)