Question

[Nguyễn Phú Đức]

giúp mk câu này với

Answer 1

[Đoàn Đức Hà]

\(\frac{4}{2\times4}+\frac{4}{4\times6}+...+\frac{4}{164\times166}\)

\(=2\times\left(\frac{2}{2\times4}+\frac{2}{4\times6}+...+\frac{2}{164\times166}\right)\)

\(=2\times\left(\frac{4-2}{2\times4}+\frac{6-4}{4\times6}+...+\frac{166-164}{164\times166}\right)\)

\(=2\times\left(\frac{1}{2}-\frac{1}{4}+\frac{1}{4}-\frac{1}{6}+...+\frac{1}{164}-\frac{1}{166}\right)\)

\(=2\times\left(\frac{1}{2}-\frac{1}{166}\right)=\frac{82}{83}\)