Question

[Nguyễn Hà Linh]

Tính nhanh : 5/2 + 5/6 + ..... + 5/486

Answer 1

[Đoàn Đức Hà]

\(A=\frac{5}{2}+\frac{5}{6}+\frac{5}{18}+\frac{5}{54}+\frac{5}{162}+\frac{5}{486}\)

\(3\times A=\frac{15}{2}+\frac{5}{2}+\frac{5}{6}+\frac{5}{18}+\frac{5}{54}+\frac{5}{162}\)

\(3\times A-A=\left(\frac{15}{2}+\frac{5}{2}+\frac{5}{6}+\frac{5}{18}+\frac{5}{54}+\frac{5}{162}\right)-\left(\frac{5}{2}+\frac{5}{6}+\frac{5}{18}+\frac{5}{54}+\frac{5}{162}+\frac{5}{486}\right)\)

\(2\times A=\frac{15}{2}-\frac{5}{486}\)

\(A=\frac{910}{243}\)