Question

Tính nhanh:

\(\frac{4}{2.4}\)+\(\frac{4}{4.6}\)+\(\frac{4}{6.8}\)+..........+\(\frac{4}{16.18}\)+\(\frac{4}{18.20}\)

giải giúp mình nha ~~~

chúc các bn học giỏi!!!!!!!!!!!!

Answer 1

Đặt \(A=\frac{4}{2.4}+\frac{4}{4.6}+\frac{4}{6.8}+...+\frac{4}{16.18}\)

\(A=\frac{4-2}{2.4}+\frac{6-4}{4.6}+\frac{8-6}{6.8}+....+\frac{18-16}{16.18}\)

\(A=\frac{4}{2}.\left(\frac{1}{2}-\frac{1}{4}+\frac{1}{4}-\frac{1}{6}+\frac{1}{6}-\frac{1}{8}+...+\frac{1}{16}-\frac{1}{18}\right)\)

\(A=\frac{4}{2}.\left(\frac{1}{2}-\frac{1}{18}\right)\)

\(A=\frac{4}{2}.\frac{4}{9}\)

\(\Rightarrow A=\frac{8}{9}\)

Answer 2

\(\frac{4}{2.4}+\frac{4}{4.6}+\frac{4}{6.8}+...+\frac{4}{16.18}\)

\(=\frac{4}{2}\left(\frac{1}{2}-\frac{1}{4}+\frac{1}{4}-\frac{1}{6}+\frac{1}{6}-\frac{1}{8}+...+\frac{1}{16}-\frac{1}{18}\right)\)

\(=2\left(\frac{1}{2}-\frac{1}{18}\right)\)

\(=2.\frac{4}{9}\)

\(=\frac{8}{9}\)