Ta có:\(\left(1-\dfrac{1}{2010}\right)\left(1-\dfrac{2}{2010}\right)\left(1-\dfrac{3}{2010}\right)...\left(1-\dfrac{2010}{2010}\right)\left(1-\dfrac{2011}{2010}\right)\)
=\(\left(1-\dfrac{1}{2010}\right)\left(1-\dfrac{2}{2010}\right)\left(1-\dfrac{3}{2010}\right)....\)0\(\left(1-\dfrac{2011}{2010}\right)=0\)
BT1: Tính
5) \(\dfrac{1}{1+\dfrac{2009}{2011}+\dfrac{2009}{2010}}+\dfrac{1}{1+\dfrac{2010}{2009}+\dfrac{2010}{2011}}+\dfrac{1}{1+\dfrac{2011}{2009}+\dfrac{2011}{2010}}\)
Tính:
D =\(\dfrac{\dfrac{2010}{1}+\dfrac{2009}{2}+\dfrac{2008}{3}+...+\dfrac{1}{2010}}{\dfrac{1}{2}+\dfrac{1}{3}+\dfrac{1}{4}+...+\dfrac{1}{2011}}\)
So sánh P và Q
\(P=\dfrac{2010}{2011}+\dfrac{2010}{2012}+\dfrac{2012}{2013};Q=\dfrac{2010+2011+2012}{2011+2012+2013}\)
Cho : A = \(\dfrac{2009^{2010}+1}{2009^{2009}+1}\)
B = \(\dfrac{2009^{2011}-2}{2009^{2010}-2}\)
Hãy so sánh A và B
Bài 1:
a. Cho a, b, m thuộc N*. So sánh 2 phân số \(\dfrac{a}{b}\) và \(\dfrac{a+m}{b+m}\)
b. Áp dụng so sánh: A = \(\dfrac{10^{1992}+1}{10^{1991}+1}\) và B = \(\dfrac{10^{1993}+1}{10^{1992}+1}\)
C = \(\dfrac{2010^{2008}+1}{2010^{2009}+1}\) và D = \(\dfrac{2010^{2007}+1}{2010^{2008}+1}\)
Thực hiện phép tính sau
\(A=1003+1007+\dfrac{2010}{113}+\dfrac{2010}{117}-\dfrac{1003}{119}-\dfrac{1007}{119}\)
_____________________________________________
\(1003+1008+\dfrac{2011}{113}+\dfrac{2011}{117}-\dfrac{1003}{119}-\dfrac{1008}{119}\)
Thực hiện phép tính
a. \(A=\dfrac{1}{10}+\dfrac{1}{15}+\dfrac{1}{21}+...+\dfrac{1}{120}\)
b. \(B=1-2+3-4+...+2007-2008+2009-2010\)
Cho M =\(\dfrac{1}{2^2}+\dfrac{1}{3^2}+\dfrac{1}{4^2}+....+\dfrac{1}{2009^2}+\dfrac{1}{2010^2}\)
\(Help\)\(me\) Hu hu hu !
BT2: Tìm x
1) \(x.\left(\dfrac{124124}{125125}-1\right)=\dfrac{2222}{5555}:\left[\left(\dfrac{2010}{2121}-1\right):\left(\dfrac{4040}{4141}-1\right)\right]\)
