\(\dfrac{1}{2^2}+\dfrac{1}{3^2}+\dfrac{1}{4^2}+...+\dfrac{1}{2014^2}< \dfrac{1}{1.2}+\dfrac{1}{2.3}+\dfrac{1}{3.4}+...+\dfrac{1}{2013.2014}=1-\dfrac{1}{2}+\dfrac{1}{2}-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{4}+...+\dfrac{1}{2013}-\dfrac{1}{2014}=1-\dfrac{1}{2014}=\dfrac{2013}{2014}\left(đpcm\right)\)
\(Cho\) \(S=1-\dfrac{1}{2}+\dfrac{1}{3}-\dfrac{1}{4}+\dfrac{1}{5}-...+\dfrac{1}{2013}-\dfrac{1}{2014}+\dfrac{1}{2015}\)
\(B=\dfrac{1}{1008}+\dfrac{1}{1009}+\dfrac{1}{1010}+...+\dfrac{1}{2014}+\dfrac{1}{2015}\)
Tính (S - B)2016
Tìm x , biết ;
\(\dfrac{x+1}{2016}+\dfrac{x+2}{2015}=\dfrac{x+3}{2014}+\dfrac{x+4}{2013}\)
Tìm x biết: \(\dfrac{x-1}{2014}+\dfrac{x-2}{2013}-\dfrac{x-3}{2012}=\dfrac{x-4}{2011}\)
Tìm x biết:
a) \(2^x+2^{x+1}+2^{x+2}+2^{x+3}=120\)
b) \(\dfrac{x+4}{2011}+\dfrac{x+3}{2012}=\dfrac{x+2}{2013}+\dfrac{x+1}{2014}\)
Tìm x biết
\(\left(\dfrac{1}{2}+\dfrac{1}{3}+...+\dfrac{1}{2015}+\dfrac{1}{2016}\right)x=\dfrac{2015}{1}+\dfrac{2014}{2}+...+\dfrac{2}{2014}+\dfrac{1}{2015}\)
Cho A = \(\dfrac{2015}{2014^2+1}+\dfrac{2015}{2014^2+2}+\dfrac{2015}{2014^3+3}+....+\dfrac{2015}{2014^2+2014}\)
Chứng minh rằng A không là số nguyên dương
Các bạn ơi , giúp mình với T T
8) \(A=\dfrac{9}{10}-\dfrac{1}{90}-\dfrac{1}{72}-\dfrac{1}{56}-\dfrac{1}{42}-\dfrac{1}{30}-\dfrac{1}{20}-\dfrac{1}{12}-\dfrac{1}{6}-\dfrac{1}{2}\)
9) \(B=\dfrac{1}{3}+\dfrac{1}{3^2}+\dfrac{1}{3^4}+...+\dfrac{1}{3^{2014}}+\dfrac{1}{3^{2015}}\)
10) \(P=\dfrac{\dfrac{1}{2}+\dfrac{1}{3}+\dfrac{1}{4}+...+\dfrac{1}{2005}}{\dfrac{2004}{1}+\dfrac{2003}{2}+\dfrac{2002}{3}+...+\dfrac{1}{2004}}\)
Tính :
\(\dfrac{1}{1}+\dfrac{1}{2}+\dfrac{1}{3}+...+\dfrac{1}{2014}+\dfrac{1}{2015}\)
Rút gọn A=\(\dfrac{\dfrac{1}{2}+\dfrac{1}{3}+\dfrac{1}{4}+...+\dfrac{1}{2013}}{2012+\dfrac{2012}{2}+\dfrac{2011}{3}+...+\dfrac{1}{2013}}\)
