\(A=\left(\dfrac{1}{2}-1\right)\left(\dfrac{1}{3}-1\right)\left(\dfrac{1}{4}-1\right)...\left(\dfrac{1}{100}-1\right)\)
\(=\left(\dfrac{-1}{2}\right).\left(\dfrac{-2}{3}\right).\left(\dfrac{-3}{4}\right)...\left(\dfrac{-99}{100}\right)\) ( 99 phân số )
\(=\dfrac{\left(-1\right)\left(-2\right)\left(-3\right)...\left(-99\right)}{2.3.4...100}=\dfrac{-1}{100}\)
Vậy \(A=\dfrac{-1}{100}\)
1: rút gọn rồi tính
\(\left(-\dfrac{72}{40}-\dfrac{144}{60}-2\dfrac{1}{3}\right)\) : \(\left(\dfrac{45}{100}-\dfrac{25}{60}+-\dfrac{75}{25}\right)\)
2: tìm x: \(3\cdot\left(4-x\right)+\left(x+2\right)\cdot\left(1+2x\right)=7\cdot\left(1+x\right)-2x\cdot\left(2-x\right)\)
3: tìm x: \(\dfrac{2\cdot\left(1+x\right)}{3}-\dfrac{5\cdot\left(2-x\right)}{6}=1\dfrac{1}{3}-\dfrac{3\cdot\left(2x+3\right)}{4}-1\dfrac{1}{2}\cdot\left(x+1\right)\)
4: cho a= \(3+3^{2^3}+3^3+3^4+...+3^{360}\)
Tính nhanh:
A= \(\left(1+\dfrac{1}{1\cdot3}\right)\cdot\left(1+\dfrac{1}{2\cdot4}\right)\cdot\left(1+\dfrac{1}{3\cdot5}\right)\cdot...\cdot\left(1+\dfrac{1}{99\cdot100}\right)\)
Tính giá trị biểu thức:
A=1-2+22-23+24-25+...+22008
B:\(\left(1+\dfrac{8}{10}\right)\cdot\left(1+\dfrac{8}{22}\right)\cdot\left(1+\dfrac{8}{36}\right)\cdot...\cdot\left(1+\dfrac{8}{8532}\right)\)
1:rút gọn
\(\dfrac{11\cdot3^{22}\cdot3^7-9^{15}}{\left(2\cdot3^{14}\right)^2}\)
2: tìm x
\(\dfrac{3\cdot\left(x-2\right)}{4}-\dfrac{2\cdot\left(1+2x\right)}{3}=1\dfrac{1}{4}-5\cdot\dfrac{\left(1+3x\right)}{6}-\dfrac{x-2}{12}\)
tính:
a) \(\left(\dfrac{1}{2}-1\right)\cdot\left(\dfrac{1}{3}-1\right)\cdot\left(\dfrac{1}{4}-1\right)\cdot...\left(\dfrac{1}{1000}-1\right)\)
b) \(\dfrac{3}{^22}\cdot\dfrac{8}{^23}\cdot\dfrac{15}{^24}\cdot...\dfrac{99}{^210}\)
giúp mik với nhék! mik đang cần gấp. 
Bài 1 : Rút gọn phân số
a)\(\dfrac{2\cdot\left(-13\right)\cdot9\cdot10}{\left(-3\right)4\cdot\left(-5\right)\cdot26}\) b)\(\dfrac{15\cdot8+15\cdot4}{12\cdot3}\)
Bài 2 : Tìm tỉ số phần trăm của 2 số sau:
a)\(1\dfrac{5}{8}v̀3\dfrac{1}{4}\) b)12,5 và 2,5
Tính : T = \(\left(1-\frac{1}{4}\right)\cdot\left(1-\frac{1}{9}\right)\cdot\left(1-\frac{1}{16}\right)\cdot....\left(1-\frac{1}{576}\right)\cdot\left(1-\frac{1}{625}\right)\)
1)tìm x\(\in\)Q biết:
a)\(\left(5\cdot x+1\right)^2=\dfrac{36}{49}\)
2)tìm x,y biết:
a)\(x^2+\left(y-\dfrac{1}{10}\right)^4=0\)
b)\(\left(\dfrac{1}{2}x-5\right)^{20}+\left(y^2-\dfrac{1}{4}\right)^{40}\le0\)
Cho B=\(\left(1-\frac{1}{2}\right)\cdot\left(1-\frac{1}{3}\right)\cdot\left(1-\frac{1}{4}\right)\cdot...\cdot\left(1-\frac{1}{20}\right)\)
So sánh B với \(\frac{1}{21}\)
