Ta có :
\(\frac{a+2015}{a-2015}=\frac{b+2016}{b-2016}\Rightarrow\frac{a+2015}{b+2016}=\frac{a-2015}{b-2016}=\frac{a+2015+a-2015}{b+2016+b-2016}=\frac{2a}{2b}=\frac{a}{b}\)
Bạn xét tích chéo là ra
1 a) CMR : Nếu \(\frac{a+2016}{a-2016}=\frac{b+2015}{b-2015}\)
Thì \(\frac{a}{2016}=\frac{b}{2015}\)
Cho 3 số dương a,b,c
\(\frac{ab}{a+b}=\frac{bc}{b+c}=\frac{ac}{a+c}\)
\(Tính:A=\frac{21ab^{2015}+12bc^{2015}+15ca^{2015}}{a^{2016}+b^{2016}+c^{2016}}\)
So sánh:
A=\(\frac{2015}{\sqrt{2016}}+\frac{2016}{\sqrt{2015}}\) và B=\(\sqrt{2015}+\sqrt{2016}\)
cho A=\(\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+.......+\frac{1}{2016}+\frac{1}{2017}\)
va B=\(\frac{2016}{1}+\frac{2015}{2}+\frac{2014}{3}+......+\frac{2}{2015}+\frac{1}{2016}\)
Tinh ti so \(\frac{A}{B}\)
a)A=\(\frac{\frac{1}{2}+\frac{1}{3}+...+\frac{1}{2012}}{\frac{2011}{1}+\frac{2010}{2}+\frac{2009}{3}+...+\frac{1}{2011}}\)
b)A =\(\frac{1}{2}+\frac{1}{3}+...+\frac{1}{2016}+\frac{1}{2017}\)và B = \(\frac{2016}{1}+\frac{2015}{2}+\frac{2014}{3}+...+\frac{2}{2015}+\frac{3}{2016}\)
Tính \(\frac{B}{A}\)
Cho A= \(\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+....+\frac{1}{2016}+\frac{1}{2017}\)
B =\(\frac{2016}{1}+\frac{2015}{2}+....+\frac{2}{2015}+\frac{1}{2016}\)
Tinh \(\frac{B}{A}\)giai ra giup minh voi
\(B=\frac{\frac{2016}{1}+\frac{2015}{2}+...+\frac{1}{2015}+\frac{1}{2016}}{\frac{1}{2}+\frac{1}{3}+...+\frac{1}{2017}}\)
So Sanh Hai Phan So Sau:
\(A=\frac{2014}{2015}-\frac{2015}{2016}+\frac{2016}{2017}-\frac{2017}{2018}\) VA \(B=-\frac{1}{2014.2015}-\frac{1}{2016.2017}\)
Cho \(A=\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+...+\frac{1}{2017};B=\frac{2016}{1}+\frac{2015}{2}+\frac{2014}{3}+...+\frac{1}{2016}\).CMR B/A là số nguyên
