Question

[Minh Nhật]

Tính : \(\frac{1}{1.3}+\frac{1}{3.5}+\frac{1}{5.7}+....+\frac{1}{19.21}\)

Answer 1

[florentino]

gọi biểu thức là A

ta có :

A = \(\frac{1}{1.3}+\frac{1}{3.5}+\frac{1}{5.7}...\frac{1}{19.21}\)

=> 2A = \(\frac{2}{1.3}+\frac{2}{3.5}+\frac{2}{5.7}...\frac{2}{19.21}\)

2A = \(\frac{1}{1}-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+...-\frac{1}{21}\)

2A = 1 - \(\frac{1}{21}\)

2A = \(\frac{20}{21}\)

A = \(\frac{20}{21}:2=\frac{10}{21}\)