Question

Tính nhanh \(\frac{2^2}{2.4}+\frac{2^2}{4.6}+...+\frac{2^2}{26.28}\)

Answer 1

\(\frac{2^2}{2.4}+\frac{2^2}{4.6}+...+\frac{2^2}{26.28}\)

= \(2.\left(\frac{2}{2.4}+\frac{2}{4.6}+...+\frac{2}{26.28}\right)\)

= \(2.\left(\frac{1}{2}-\frac{1}{4}+\frac{1}{4}-\frac{1}{6}+...+\frac{1}{26}-\frac{1}{28}\right)\)

= \(2.\left(\frac{1}{2}-\frac{1}{28}\right)\)

= \(2.\frac{13}{28}\)

= \(\frac{13}{14}\)

Answer 2

\(=2\left(\frac{2}{2.4}+\frac{2}{4.6}+...+\frac{2}{26.28}\right)=2\left(\frac{1}{2}-\frac{1}{4}+\frac{1}{4}-\frac{1}{6}+...+\frac{1}{26}-\frac{1}{28}\right)\)

\(=2\left(\frac{1}{2}-\frac{1}{28}\right)\)

Answer 3

\(=\frac{1}{1.2}+\frac{1}{2.3}+...+\frac{1}{13.14}\)

\(=1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+...+\frac{1}{13}-\frac{1}{14}\)

\(=1-\frac{1}{14}=\frac{13}{14}\)