Question

Tinh nhanh:

\(\frac{7}{1\cdot5}+\frac{7}{5\cdot9}+\frac{7}{9\cdot13}+\frac{7}{13\cdot17}+\frac{7}{17\cdot21}\)

Answer 1

 = 7/4.(4/1.5 + 4/5.9 + 4/9.13 + 4/13.17 + 4/17.21)

 = 7/4.(1-1/5+1/5-1/9+1/9-1/13+1/13-1/17+1/17-1/21)

 = 7/4.(1-1/21)

 = 7/4.20/21 = 5/3

Tk mk nha

Answer 2

Đặt biểu thức bằng A

4/7A=1-1/5+1/5-1/9+...+1/17_1/21

4/7A=1-1/21

4/7A=20/21

A=35/21=5/3

Answer 3

Dễ ấy  mà

Answer 4

đặt \(A=\frac{7}{1.5}+\frac{7}{5.9}+\frac{7}{9.13}+\frac{7}{13.17}+\frac{7}{17.21}\)

\(\frac{4}{7}A=\frac{4}{1.5}+\frac{4}{5.9}+\frac{4}{9.13}+\frac{4}{13.17}+\frac{4}{17.21}\)

\(\frac{4}{7}A=1-\frac{1}{5}+\frac{1}{5}-\frac{1}{9}+\frac{1}{9}-\frac{1}{13}+\frac{1}{13}-\frac{1}{17}+\frac{1}{17}-\frac{1}{21}\)

\(\frac{4}{7}A=1-\frac{1}{21}\)

\(\frac{4}{7}A=\frac{20}{21}\)

\(\Rightarrow A=\frac{20}{21}\div\frac{4}{7}\)

\(\Rightarrow A=\frac{5}{3}\)