Question

[Online_ Math]

1/ Tìm x :

\(\frac{x\times2+5}{x+5}=\frac{6}{4}\)

2/ Tính nhanh :

a) \(\frac{4}{1\times5}+\frac{4}{5\times9}+\frac{4}{9\times13}+\frac{4}{13\times17}+\frac{4}{17\times21}\)

b) \(\left(1-\frac{1}{2}\right)\times\left(1-\frac{1}{3}\right)\times\left(1-\frac{1}{4}\right)\times.......\times\left(1-\frac{1}{2017}\right)\)

c) \(A=2000-5-5-5-.......-5\)( có 200 số 5 )

Answer 1

[Đức Phạm]

2/ 

a) \(\frac{4}{1\cdot5}+\frac{4}{5\cdot9}+\frac{4}{9\cdot13}+\frac{4}{13\cdot17}+\frac{4}{17\cdot21}\)

\(=\left(1-\frac{1}{5}+\frac{1}{5}-\frac{1}{9}+....+\frac{1}{17}-\frac{1}{21}\right)\)

\(=1-\frac{1}{21}=\frac{20}{21}\)

b) \(\left(1-\frac{1}{2}\right)\cdot\left(1-\frac{1}{3}\right)\cdot\left(1-\frac{1}{4}\right)\cdot...\cdot\left(1-\frac{1}{2017}\right)\)

\(=\frac{1}{2}\cdot\frac{2}{3}\cdot\frac{3}{4}\cdot..\cdot\frac{2016}{2017}\)

\(=\frac{1}{2017}\)

c) \(A=2000-5-5-5-..-5\)(có 200 số 5) 

\(A=2000-\left(5\cdot200\right)\)

\(A=2000-1000\)

\(A=1000\)