Question

Tính hợp lí

A = 4/4.7 + 4/7.10 + ...... + 4/79.82

Answer 1

\(4\left(\frac{1}{4.7}+\frac{1}{7.10}+...+\frac{1}{79.82}\right)\)

\(=\frac{4}{3}\left(\frac{3}{4.7}+\frac{3}{7.10}+...+\frac{3}{79.8}\right)\)

\(=\frac{4}{3}\left(\frac{1}{4}-\frac{1}{7}+\frac{1}{7}-\frac{1}{10}+...+\frac{1}{79}-\frac{1}{82}\right)\)

\(=\frac{4}{3}\left(\frac{1}{4}-\frac{1}{82}\right)\)

\(=\frac{4}{3}.\frac{39}{164}=\frac{13}{41}\)