\(\left(1-\frac{1}{2010}\right).\left(1-\frac{2}{2010}\right).\left(1-\frac{3}{2010}\right)...\left(1-\frac{2011}{2010}\right)\)

\(=\left(1-\frac{1}{2010}\right).\left(1-\frac{2}{1010}\right).\left(1-\frac{3}{2010}\right)....\left(1-\frac{2010}{2010}\right).\left(1-\frac{2011}{2010}\right)\)

\(=\left(1-\frac{1}{2010}\right).\left(1-\frac{2}{2010}\right).\left(1-\frac{3}{2010}\right)...\left(1-1\right).\left(1-\frac{2011}{2010}\right)\)

\(=\left(1-\frac{1}{2010}\right).\left(1-\frac{2}{2010}\right).\left(1-\frac{3}{2010}\right)...0.\left(1-\frac{2011}{2010}\right)\)

\(=0\)

Ta có :

\(A=\left(2010.2010^{2010}+2010.2011^{2010}\right)^{2010}+\left(2011.2010^{2010}+2011.2011^{2010}\right)^{2010}\)

\(\Rightarrow\left(2010.2010^{2010}+2011.2011^{2010}\right)^{2010}=B\)

Có : \(2009+2010>\dfrac{2009}{2010}\) ; \(2011+2012>\dfrac{2011}{2012}\)

\(\dfrac{2011}{2010}>1\) ; \(\dfrac{2010}{2011}< 1\) \(\Rightarrow\dfrac{2011}{2010}>\dfrac{2010}{2011}\)

Ta có : \(2009+2010+\dfrac{2011}{2010}+2011+2012>\dfrac{2009}{2010}+\dfrac{2010}{2011}+\dfrac{2011}{2012}\)

\(\Leftrightarrow B>A\)

Hay \(A< B\)

ủng hộ mình lên 290 với các bạn

mk sử dụng điện thoại đc ko?? So sánh cái j vs cái j???

Ơ! Có mỗi cái vế A thì làm sao so sánh đc hả bạn? Bạn xem lại xem có thiếu đề ko vậy??

M<N

\(N=\left(2010^{2010}+2011^{2010}\right)^{2011}=\left(2010^{2010}+2011^{2010}\right)^{2010}.\left(2010^{2010}+2011^{2010}\right)\)

\(>\left(2010^{2010}+2011^{2010}\right)^{2010}.2011^{2010}=\left[\left(2010^{2010}+2011^{2010}\right)2011\right]^{2010}\)

\(>\left(2010^{2010}.2010+2011^{2010}.2011\right)^{2010}=\left(2010^{2011}+2011^{2011}\right)^{2010}=M\)

Vậy M < N,