Question

[Nguyễn Thuy Lan]

2/1.2 + 2/2.3 + 2/3.4 + .....+2/18.19 + 2/19.20

Answer 1

[Cô nàng cự giải]

Đặt \(A=\frac{2}{1.2}+\frac{2}{2.3}+\frac{2}{3.4}+...+\frac{2}{18.19}+\frac{2}{19.20}\)

\(\Rightarrow A=2.\left(1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{18}-\frac{1}{19}+\frac{1}{19}-\frac{1}{20}\right)\)

\(\Rightarrow A=2.\left(1-\frac{1}{20}\right)\)

\(\Rightarrow A=2.\frac{19}{20}\)

\(\Rightarrow A=\frac{19}{10}\)

Answer 2

[FIFA MOBIE]

2.(1/1.2+1/2.3+.....+1/18.19+1/19.20)

2.(1/1-1/2+1/2-1/3+......+1/19-1/20)

2.(1/1-1/20)= 2.19/20=19/10