Question

[Phạm Thị Minh Nguyệt]

Tính nhanh biểu thức sau: 5/3x4 + 5/4x5 + 5/5x6+....... + 5/25x26+ 5/26x27

Answer 1

[Đức Phạm]

\(\frac{5}{3\times4}+\frac{5}{4\times5}+\frac{5}{5\times6}+...+\frac{5}{25\times26}+\frac{5}{26\times27}\)

\(=\frac{4-3}{3\times4}+\frac{5-4}{4\times5}+\frac{6-5}{5\times6}+...+\frac{26-25}{25\times26}+\frac{27-26}{26\times27}\)

\(=5\times\left(\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+\frac{1}{5}-\frac{1}{6}+....+\frac{1}{25}-\frac{1}{26}+\frac{1}{26}-\frac{1}{27}\right)\)

\(=5\times\left(\frac{1}{3}-\frac{1}{27}\right)\)

\(=5\times\frac{8}{27}=\frac{40}{27}\)

Answer 2

[Trịnh Thành Công]

\(\frac{5}{3.4}+\frac{5}{4.5}+\frac{5}{5.6}+...+\frac{5}{25.26}+\frac{5}{26.27}\)

\(=5\left(\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+...+\frac{1}{25}-\frac{1}{26}+\frac{2}{26}-\frac{1}{27}\right)\)

\(=5\left(\frac{1}{3}-\frac{1}{27}\right)\)

\(=\frac{40}{27}\)