\(\dfrac{1}{2001.2003}+\dfrac{1}{2003.2005}+...+\dfrac{1}{2011.2013}\)

\(=\dfrac{1}{2}\left(\dfrac{2}{2001.2003}+\dfrac{1}{2003.2005}+...+\dfrac{1}{2011.2013}\right)\)

\(=\dfrac{1}{2}\left(\dfrac{1}{2001}-\dfrac{1}{2003}+\dfrac{1}{2003}-\dfrac{1}{2005}+...+\dfrac{1}{2011}-\dfrac{1}{2013}\right)\)

\(=\dfrac{1}{2}\left(\dfrac{1}{2001}-\dfrac{1}{2013}\right)=\dfrac{2}{1342671}\)

=1/2.(2/2001.2003+2/2003.2005+.....+2/2011.2013)

=1/2(1/2001-1/2003+1/2003-1/2005+....+1/2011-1/2013)

=1/2(1/2001-1/2013)

=2/1342671

\(A=\frac{2012\times2013-1}{2011\times2013+2012}\)

\(A=\frac{2012\times2013-1}{2011\times2013+2011+1}\)

\(A=\frac{2012\times2013-1}{2013\times\left(2011+1\right)+1}\)

\(A=\frac{2012\times2013-1}{2013\times2012+1}\)

\(A=\frac{2012\times2013+1-2}{2012\times2013+1}\)

\(A=1-\frac{2}{2012\times2013+1}\)

Tính tử số 2012x2013-1=2011x2013+2013-1=2011x2013+2012

Do tử=mẫu =2011x2013=2012

Suy ra: A=1

Trả lời

2012.2013-1/2011.2013+2012

=2011.2013+2012-1/2011.2013+2012

=-1/1

=-1.

Học tốt !

\(\frac{2012.2013-1}{2011.2013+2012}\)

\(=\frac{2012.2013-1}{\left(2012-1\right)\left(2012+1\right)+2012}\)

\(=\frac{2012.2013-1}{2012^2-1^2+2012}\)

\(=\frac{2012.2013-1}{2012.2013-1}\)

\(=1\)

Chúc em học tốt !!!

Xx(2013+1/2013)=1/2013+2013

X=(1/2013+2013):(1/2013+2013)

X=1

\(.A=\frac{1}{2}.\left(\frac{1}{5}-\frac{1}{7}+\frac{1}{7}-\frac{1}{9}+...+\frac{1}{2011}-\frac{1}{2013}\right)\)

\(A=\frac{1}{2}.\left(\frac{1}{5}-\frac{1}{2013}\right)\)

\(A=\frac{1004}{10065}\)

<a class="ptip tipped" data-name="Nguyễn Ngọc Sáng" data-image="http://olm.vn/images/avt/avt424601_60by60.jpg" href="/thanhvien/nguyenngocsang6a" data-uid="125744" data-hasqtip="true" aria-describedby="qtip-2"> Sáng Nguyễn </a>

A=1/5x7+11/7x9+1/9x11+....+1/2011x2013

2xA=2x(1/5x7+1/7x9+1/9x11+...+1/2011x2013

2xA=2/5x7+2/7x9+2/9x11+...+2/2011x2013

2xA=1/5-1/7+1/7-1/9+1/9-1/11+...+1/2011-1/2013

2xA=1/5-1/2013

2xA=2013/10045-5/10045

2xA=2008/10045

A=2008/10045:2

A=2008/10045x1/2

A=1004/10045

\(2013.x+x.\frac{1}{2013}-2013=\frac{1}{2013}\)

\(x.\left(2013+\frac{1}{2013}\right)=\frac{1}{2013}+2013\)

\(x=\left(\frac{1}{2013}+2013\right):\left(2013+\frac{1}{2013}\right)\)

\(x=1\)

chúc bạn học tốt

\(2013.y+y.\frac{1}{2013}-2013=\frac{1}{2013}\)

\(\Rightarrow2013.y+y.\frac{1}{2013}=\frac{1}{2013}+2013\)

\(\Rightarrow y.\left(2013+\frac{1}{2013}\right)=2013+\frac{1}{2013}\)

\(\Rightarrow y=1\)

khó thế 

(1-2+3-4+.....-98+99)x(2013x6-2013-2013x5)

=(1-2+3-4+....-98+99)x[ 2013x(6-1-5)]

= (1-2+3-4+....-98+99)x(2013x0)

= (1-2+3-4+....-98+99)x0 = 0

Chỉ cần rút gọn:

2011x2013-2012x2011=2011x(2013-2012)=2011

2011x2012+2011x2013=2011x2012-2011x(-2013)=2011x(2012-(-2013)

Ra phân số là:\(\frac{1}{4025}\)

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