Cho a =\(\frac{1+\left(1+2\right)+\left(1+2+3\right)+...+\left(1+2+3+...+2012\right)}{2012x1+2011x2+201x3+...+2x2011+1x2012}\)

tính A=1x2012+2x2011+3x2010+...+2012x1

 1+(1+2)+(1+2+3)+(1+2+3+4)+...+(1+2+3+4+...+2012)

1x2012+2x2012+3x2010+....+2012x1

tinh gia tri bieu thuc tren.(giai giup minh voi,dang voi)

cho \(f\left(x\right)=\dfrac{x^3}{1-3x-3x^2}\). hãy tính giá trị biểu thức sau: \(A=f\left(\dfrac{1}{2012}\right)+f\left(\dfrac{2}{2012}\right)+...+f\left(\dfrac{2010}{2012}\right)+f\left(\dfrac{2011}{2012}\right)\)

Tính nhanh: \(\left(2012\times2010+2010\times2008\right)\times\left(1+\dfrac{1}{2}\div1\dfrac{1}{2}-1\dfrac{1}{3}\right)\)

ĐỀ : Tính

\(M=\dfrac{\left(1+\dfrac{2012}{1}\right)\left(1+\dfrac{2012}{1}\right)...\left(1+\dfrac{2012}{1000}\right)}{\left(1+\dfrac{1000}{1}\right)\left(1+\dfrac{1000}{2}\right)...\left(1+\dfrac{1000}{2012}\right)}\)

Mong mọi người giúp đỡ ❤ !

Tính

P=\(\left(1-\dfrac{28}{10}\right)\left(1-\dfrac{52}{22}\right)\left(1-\dfrac{80}{36}\right)...\left(1-\dfrac{21808}{10900}\right)\)

Q=\(\dfrac{1+\dfrac{1}{2}+\dfrac{1}{3}+...+\dfrac{1}{2012}}{\dfrac{2013}{1}+\dfrac{2014}{2}+\dfrac{2015}{3}+...+\dfrac{4023}{2011}+\dfrac{4024}{2012}-2012}\)

Tính

a) \(\left(1-\dfrac{1}{2}\right).\left(1-\dfrac{1}{3}\right).\left(1-\dfrac{1}{4}\right).....\left(1-\dfrac{1}{2012}\right)\)

Cho \(x=\sqrt{\dfrac{1}{2\sqrt{3}-2}-\dfrac{3}{2.\left(\sqrt{3}+1\right)}}\). Tính: \(A=\dfrac{4.\left(x+1\right).x^{2013}-2.x^{2012}+2x+1}{2x^2+3x}\)