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\(=\frac{\left(1.2.3.....2014\right)}{\left(2.3.4.5.6....2015\right)}=\frac{1}{2015}\)
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Đặt phân thức trên là D
=> D=(1+1+1+1+...+1+2013/2+2012/3+...+2/2013+1/2014)/(1/2+1/3+1/4+...+1/2014)
=> D=(1+2013/2+1+2012/3+1+2011/4+...+1+2/2013+1+1/2014+1)/(1/2+1/3+1/4+1/5+...+1/2014)
=> D=(2015/2+2015/3+2015/4+...+2015/2013+2015/2014+1)/(1/2+1/3+1/4+...+1/2014)
=> D=[2015*(1/2+1/3+1/4+1/5+....+1/2014)]/(1/2+1/3+1/4+1/5+...+1/2014)
=> D=2015
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Ta có:
\(=\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+...+\frac{1}{2013.2014}\)
Ta thấy :
\(\frac{1}{1.2}=\frac{1}{1}-\frac{1}{2}\)
\(\frac{1}{2.3}=\frac{1}{2}-\frac{1}{3}\)
\(...\)
\(\frac{1}{2013.2014}=\frac{1}{2013}-\frac{1}{2014}\)
Ta có:
\(=\frac{1}{1}-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+...+\frac{1}{2013}-\frac{1}{2014}\)
\(=1-\frac{1}{2014}\)
\(=\frac{2013}{2014}\)
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tớ cần gấp !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
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1+2+3+4+...+2013+2014
=(2014+1)x2014:2
=2015x2014:2
=2029105
Chúc bạn học giỏi nha!!!
\(=\frac{\left(2014+1\right).2014}{2}=2029105\)