Tính
\(A=\left(\dfrac{1}{5}+\dfrac{2013}{2014}+\dfrac{2015}{2016}+1\right)\left(\dfrac{2013}{2014}+\dfrac{2015}{2016}+\dfrac{1}{10}\right)-\left(\dfrac{1}{5}+\dfrac{2013}{2014}+\dfrac{2015}{2016}\right)\left(\dfrac{2013}{2014}+\dfrac{2015}{2016}+\dfrac{1}{10}+1\right)\)
Tìm x:
\(\left(\dfrac{1}{2}+\dfrac{1}{3}+.....+\dfrac{1}{2014}\right)x=\dfrac{2013}{1}+\dfrac{2012}{2}+.....+\dfrac{2}{2012}+\dfrac{1}{2013}\)
Cho x, y, z thỏa mãn \(\dfrac{x}{2013}=\dfrac{y}{2014}=\dfrac{z}{2015}\). Chứng minh rằng: \(\left(x-z\right)^3=8\cdot\left(x-y\right)^2\left(y-z\right)\)
Cho :S=\(1-\dfrac{1}{2}+\dfrac{1}{3}-\dfrac{1}{4}+.......+\dfrac{1}{2013}-\dfrac{1}{2014}+\dfrac{1}{2015}\) và P=\(\dfrac{1}{1008}+\dfrac{1}{1009}+......+\dfrac{1}{2014}+\dfrac{1}{2015}\) Tính \(\left(S-P\right)^{2016}\)
Tìm x
a)\(\dfrac{x+1}{10}+\dfrac{x+1}{11}+\dfrac{x+1}{12}=\dfrac{x+1}{13}+\dfrac{x+1}{14}\)
b)\(\dfrac{x+4}{2014}+\dfrac{x+3}{2015}=\dfrac{x+2}{2016}+\dfrac{x+1}{2017}\)
CẢM ƠN CÁC BẠN NHÌU ^_^
Bài 1: a) Cho \(A=\left(\dfrac{1}{2}-1\right)\left(\dfrac{1}{3}-1\right)...\left(\dfrac{1}{2015}-1\right)\left(\dfrac{1}{2016}-1\right)\). So sánh A với \(\dfrac{-1}{2015}\)
b) Cho biểu thức \(A=\dfrac{3x^3-x^2-3x+2015}{3x^4-x^3+3x+2014}\). Tính giá trị của biểu thức với x=\(\dfrac{1}{3}\)
Tìm x biết :
a) \(\dfrac{3x+2}{5x+7}=\dfrac{3x-1}{5x+1}\)
b) \(\dfrac{x+1}{2016}+\dfrac{x}{2017}=\dfrac{x+2}{2015}+\dfrac{x+3}{2014}\)
c) (2x - 1 )2 = ( 2x - 1 )2018
d) ( x - 1 )x + 2 = ( x - 1 )x + 4
e) ( 2x - 3 )2 = 144
Xét tổng T= \(\dfrac{2}{2^1}+\dfrac{3}{2^2}+\dfrac{4}{2^2}+....+\dfrac{2015}{2^{2014}}\). Hãy so sánh T với 3
Tìm x biết:
\(\dfrac{x+y}{2012}=\dfrac{xy}{2013}=\dfrac{x-y}{2014}\)