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A=\(\frac{1}{2}\).\(\frac{2}{3}\)....\(\frac{2012}{2013}\)=\(\frac{1}{2013}\)
B=\(\frac{2012}{2012.2013}\)=\(\frac{1}{2013}\)
vậy A=B
\(=\frac{2008+2009.2010}{2010.\left(2009+2\right)-2012}\)
\(=\frac{2009.2010+2008}{2010.2009+2010.2-2012}\)
\(=\frac{2008+2009.2010}{2008+2009.2010}=1\)
\(MS=2011.2013+2012\)
\(=\left(2012-1\right).2013+2012\)
\(=2012.2013-2013+2012\)
\(=2013.2012-1\)
\(=TS\)
Vậy phân số đã cho bằng 1.
Trả lời:
\(\frac{2013.2012-1}{2011.2013+2012}=\frac{2013.\left(2011+1\right)-1}{2011.2013+2012}\)
\(=\frac{2011.2013+2013-1}{2011.2013+2012}\)
\(=\frac{2011.2013+2012}{2011.2013+2012}\)
\(=1\)
Học tốt
\(\frac{2010\cdot2011+1000}{2012\cdot2010-1010}\)
= \(\frac{2010\cdot2011+1000}{\left(2011+1\right)\cdot2010-1010}\)
= \(\frac{2010\cdot2011+1000}{2011\cdot2010+2010-1010}\)
= \(\frac{2010\cdot2011+1000}{2011\cdot2010+1000}\)
= 1
\(\frac{2010.2011+1000}{2012.2010-1010}\)
\(=\frac{2010.2011+2010-1010}{2012.2010-1010}\)
\(=\frac{2010.\left(2011+1\right)-1010}{2012.2010-1010}\)
\(=\frac{2010.2012-1010}{2012.2010-1010}\)
\(=1\)
\(A=\frac{2013.2012-1}{2011.2013+2012}\)
\(A=\frac{2013\left(2011+1\right)-1}{2011.2013+2012}\)
\(A=\frac{2013.2011+2013-1}{2011.2013+2012}\)
\(A=\frac{2013.2011+2012}{2011.2013+2012}\)
\(A=1\)
$\frac{\frac{2010}{2011}}{\frac{2012}{2013}}+\frac{\frac{2011}{2012}}{\frac{2013}{2014}}+\frac{\frac{2012}{2013}}{\frac{2014}{2015}}$
$\frac{\frac{2010}{2011}}{\frac{2012}{2013}}+\frac{\frac{2011}{2012}}{\frac{2013}{2014}}+\frac{\frac{2012}{2013}}{\frac{2014}{2015}}$
$\frac{\frac{2010+2011+2012}{2011+2012+2013}}{\frac{2012+2013+2014}{2013+2014+2015}}$
$\frac{\frac{2010}{2011}+\frac{2011}{2012}+\frac{2012}{2013}}{\frac{2012+2013+2014}{2013+2014+2015}}$
$\frac{\frac{2010+2011+2012}{2011+2012+2013}}{\frac{2012}{2013}+\frac{2013}{2014}+\frac{2014}{2015}}$
\(\frac{2012.2011+2012.11+2000}{2013.2011-2011.2012}=\frac{2012.\left(2011+11\right)+2000}{2011.\left(2013-2012\right)}\)
\(=\frac{2012.2022+2000}{2011}\)
\(=\frac{4068264+2000}{2011}\)
\(=\frac{4070264}{2011}\)
\(=2024\)
~~ HỌC TỐT ~~ !! >-<