Question

\(\frac{4}{3.5}+\frac{4}{5.7}+....+\frac{4}{97.99}\)

tính tổng

Answer 1

Ta có : 

\(\frac{4}{3.5}+\frac{4}{5.7}+\frac{4}{7.9}+...+\frac{4}{97.99}\)

\(=\)\(2\left(\frac{2}{3.5}+\frac{2}{5.7}+\frac{2}{7.9}+...+\frac{2}{97.99}\right)\)

\(=\)\(2\left(\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+\frac{1}{7}-\frac{1}{9}+...+\frac{1}{97}-\frac{1}{99}\right)\)

\(=\)\(2\left(\frac{1}{3}-\frac{1}{99}\right)\)

\(=\)\(2.\frac{32}{99}\)

\(=\)\(\frac{64}{99}\)

Chúc bạn học tốt ~