Question

Tính tổng:S=5/6+11/12+19/20+...+89/90

Answer 1

\(\frac{5}{6}+\frac{11}{12}+\frac{19}{20}+....+\frac{89}{90}\)

\(S=\left(1-\frac{1}{6}\right)+\left(1-\frac{1}{12}\right)+\left(1-\frac{1}{20}\right)+....+\left(1-\frac{1}{90}\right)\)

\(S=\left(1-\frac{1}{2.3}\right)+\left(1-\frac{1}{3.4}\right)+\left(1-\frac{1}{4.5}\right)+....+\left(1-\frac{1}{9.10}\right)\)

\(S=\left(1+1+1+....+1\right)-\left(\frac{1}{2.3}+\frac{1}{3.4}+\frac{1}{4.5}+...+\frac{1}{9.10}\right)\)

\(S=8-\left(\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{9}-\frac{1}{10}\right)\)

\(S=8-\left(\frac{1}{2}-\frac{1}{10}\right)\)

\(S=8-\frac{2}{5}=\frac{38}{5}\)