Question

tinh nhanh

\(\frac{5}{2}+\frac{5}{6}+\frac{5}{12}+...+\frac{5}{90}\)= ?

Answer 1

\(\frac{5}{2}+\frac{5}{6}+\frac{5}{12}+...+\frac{5}{90}\)

\(=5.\left(\frac{1}{2}+\frac{1}{6}+\frac{1}{12}+...+\frac{1}{90}\right)\)

\(=5.\left(\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+...+\frac{1}{9.10}\right)\)

\(=5.\left(1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{9}-\frac{1}{10}\right)\)

\(=5.\left(1-\frac{1}{10}\right)\)\

\(=5.\frac{9}{10}\)

\(=\frac{9}{2}\)