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Xét tử: \(2015+\frac{2014}{2}+\frac{2013}{3}+...+\frac{1}{2015}\)
\(=\left(1+1+...+1\right)+\frac{2014}{2}+\frac{2013}{3}+...+\frac{1}{2015}\)( trong ngoặc có 2015 số 1 )
\(=\left(1+\frac{2014}{2}\right)+\left(1+\frac{2013}{3}\right)+...+\left(1+\frac{1}{2015}\right)+1\)
\(=\frac{2016}{2}+\frac{2016}{3}+\frac{2016}{4}+...+\frac{2016}{2015}+\frac{2016}{2016}\)
\(=2016\cdot\left(\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+...+\frac{1}{2016}\right)\)
Ghép tử và mẫu \(\frac{2016\cdot\left(\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+...+\frac{1}{2016}\right)}{\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+...+\frac{1}{2016}}=2016\)
Vậy \(A=2016\)
Câu b:
\(\frac{21}{8}:\frac{5}{6}+\frac{1}{2}:\frac{5}{6}\)
= \(\frac{63}{20}+\frac{3}{5}\)
= \(\frac{15}{4}\)
\(\left(\frac{21}{8}+\frac{1}{2}\right):\frac{5}{6}\)
\(\frac{25}{8}:\frac{5}{6}\)
\(\frac{25}{8}.\frac{6}{5}\)
\(\frac{30}{8}\)
a) ta có: \(A=\frac{2017.2018-1}{2017.2018}=\frac{2017.2018}{2017.2018}-\frac{1}{2017.2018}=1-\frac{1}{2017.2018}\)
\(B=\frac{2018.2019-1}{2018.2019}=1-\frac{1}{2018.2019}\)
\(\Rightarrow\frac{1}{2017.2018}>\frac{1}{2018.2019}\)
\(\Rightarrow1-\frac{1}{2017.2018}< 1-\frac{1}{2018.2019}\)
=> A < B
a)A= 2017*2018/2017*2018-1/2017*2018=1-1/2017*2018
B = 2018*2019/2018*2019-1/2018*2019=1-1/2018*2019
vì 1/2017*2018>1/2018*2019=> A<B
b)
1-\(\frac{1}{2}\)+ \(\frac{1}{3}\) - \(\frac{1}{4}\)+...+\(\frac{1}{2013}\)- \(\frac{1}{2014}\)
=(1+\(\frac{1}{3}\)+...+\(\frac{1}{2013}\)) - (\(\frac{1}{2}\)+ \(\frac{1}{4}\) + ...+ \(\frac{1}{2014}\))
=(1+\(\frac{1}{2}\)+ \(\frac{1}{3}\)+ \(\frac{1}{4}\)+...+ \(\frac{1}{2013}\)+ \(\frac{1}{2014}\))-2.(\(\frac{1}{2}\)+ \(\frac{1}{4}\)+...+\(\frac{1}{2014}\))
=1+\(\frac{1}{2}\)+ \(\frac{1}{3}\)+ \(\frac{1}{4}\)+ \(\frac{1}{2013}\)+ \(\frac{1}{2014}\)- 1-\(\frac{1}{2}\)-...-\(\frac{1}{1007}\)
=(1+\(\frac{1}{2}\)+ \(\frac{1}{3}\)+ \(\frac{1}{4}\)+...+\(\frac{1}{1007}\))+\(\frac{1}{1008}\)+ \(\frac{1}{1009}\)+...+\(\frac{1}{2013}\)+ \(\frac{1}{2014}\)-(1+\(\frac{1}{2}\)+...+\(\frac{1}{1007}\))
=\(\frac{1}{1008}\)+ \(\frac{1}{1009}\)+...+\(\frac{1}{2013}\)+ \(\frac{1}{2014}\).
mình chưa hiểu lắm
tại sao nhân 2 lên và còn 1 - \(\frac{1}{2}\)- ... - \(\frac{1}{1007}\)
1007 ở đâu?????
tớ cần gấp !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
A = 1 / 1008 + 1 / 2013 - 1 / 2016 x 2017
A = 1 / 1008 + 1 / 2013 - 1 / 2016 x 1 / 2017
B = 1 / 2014 + 1 / 2016 + 1 / 2017 + 1 / 2014 x 2016
B = 1 / 2014 + 1 / 2016 + 1 / 2017 + 1 / 2014 x 1 / 2016