Question

Tính nhanh A=\(\frac{1}{2.4}+\frac{1}{4.6}+...+\frac{1}{26.28}\)

Answer 1

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

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

\(2.A=\frac{1}{2}-\frac{1}{28}=\frac{26}{56}=\frac{13}{28}\)=> A = \(\frac{13}{56}\)