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Vì \(2014.2015=2014.2015\)nên \(2014.2015-1< 2014.2015\)1 đơn vi
Vì \(2015.2016=2015.2016\)nên \(2015.2016-1< 2015.2016\)1 đơn vị
Ta có :
\(1-M=1-\frac{2014.2015-1}{2014.2015}=\frac{1}{2014.2015}\)
\(1-N=1-\frac{2015.2016-1}{2015.2016}=\frac{1}{2015.2016}\)
Vì \(2015=2015\)nên \(2014.2015< 2015.2016\)
Vì \(\frac{1}{2014.2015}>\frac{1}{2015.2016}\)( do \(2014.2015< 2015.2016\))
Nên \(N>M\)
Vậy \(N>M\)
a.\(\frac{2015.2016-1}{2015.2016}=1-\frac{1}{2015.2016}\)
\(\frac{2016.2017-1}{2016.2017}=1-\frac{1}{2016.2017}\)
vì \(\frac{1}{2015.2016}>\frac{1}{2016.2017}\)
=>\(-\frac{1}{2015.2016}< -\frac{1}{2016.2017}\)
=>\(1-\frac{1}{2015.2016}< 1-\frac{1}{2016.2017}\)
a) So sánh \(\frac{461}{456}\) và \(\frac{128}{123}\):
\(\frac{461}{456}\) = \(\frac{456+5}{456}=1+\frac{5}{456};\frac{128}{123}=\frac{123+5}{123}=1+\frac{5}{123}\)
Vì \(\frac{1}{456}
\(\frac{1}{1\cdot2}+\frac{1}{2\cdot3}+\frac{1}{3\cdot4}+...+\frac{1}{2016\cdot2017}\)
\(=1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{2016}-\frac{1}{2017}\)
\(=1-\frac{1}{2017}=\frac{2016}{2017}\)
\(A=\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+.....+\frac{1}{2016.2017}\)
\(A=\left(\frac{1}{1}-\frac{1}{2}\right)+\left(\frac{1}{2}-\frac{1}{3}\right)+......+\left(\frac{1}{2016}-\frac{1}{2017}\right)\)
\(A=\frac{1}{1}-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+....+\frac{1}{2016}-\frac{1}{2017}\)
\(A=\frac{1}{1}-\frac{1}{2017}\)
\(A=\frac{2016}{2017}\)
A=\(\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+.....+\frac{1}{2016.2017}\)
\(\Rightarrow A=1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+......+\frac{1}{2016}-\frac{1}{2017}\)
\(\Rightarrow A=1-\frac{1}{2017}\)
\(\Rightarrow A=\frac{2016}{2017}\)
