Question

Tính nhanh :\(C=\frac{2}{3.5}+\frac{2}{5.7}+\frac{2}{7.9}+...+\frac{2}{37.39}\)

Answer 1

\(\frac{2}{3.5}+\frac{2}{5.7}+\frac{2}{7.9}+...+\frac{2}{37.39}\)

\(=\frac{2}{3}-\frac{2}{5}+\frac{2}{5}-\frac{2}{7}+\frac{2}{7}-\frac{2}{9}+...+\frac{2}{37}-\frac{2}{39}\)

\(=\frac{2}{3}-\frac{2}{39}\)

\(=\frac{8}{13}\)

Answer 2

Ta có:

\(\frac{2}{3.5}=\frac{1}{3}-\frac{1}{5}\)

\(\frac{2}{5.7}=\frac{1}{5}-\frac{1}{7}\)

\(\frac{2}{7.9}=\frac{1}{7}-\frac{1}{9}\)

\(......................................\)

\(\frac{2}{37.39}=\frac{1}{37}-\frac{1}{39}\)

nên \(C=\frac{2}{3.5}+\frac{2}{5.7}+\frac{2}{7.9}+...+\frac{2}{37.39}=\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+\frac{1}{7}-\frac{1}{9}+...+\frac{1}{37}-\frac{1}{39}\)

\(C=\frac{1}{3}-\frac{1}{39}=\frac{4}{13}\)