2014 + 2014/(1+2) + 2014/(1+2+3) + ... + 2014/(1+2+...+2013)
TN
Những câu hỏi liên quan
(1/2012+1/2013-1/2014)/(5/2012+5/2013-5/2014)-(2/2103+2/2014-2/2015)/(3/2013+3/2014-3/2015)
\(\frac{\frac{1}{2012}+\frac{1}{2013}-\frac{1}{2014}}{\frac{5}{2012}+\frac{5}{2013}-\frac{5}{2014}}-\frac{\frac{2}{2013}+\frac{2}{2014}-\frac{2}{2015}}{\frac{3}{2013}+\frac{3}{2014}-\frac{3}{2015}}\)
=\(\frac{\frac{1}{2012}+\frac{1}{2013}-\frac{1}{2014}}{5\left(\frac{1}{2012}+\frac{1}{2013}-\frac{1}{2014}\right)}-\frac{2\left(\frac{1}{2013}+\frac{1}{2014}-\frac{1}{2015}\right)}{3\left(\frac{1}{2013}+\frac{1}{2014}-\frac{1}{2015}\right)}=\frac{1}{5}-\frac{2}{3}=\frac{3}{15}-\frac{10}{15}=-\frac{7}{15}\)
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A=2014+[2014:(1+2)]+[2014:(1+2+3)]+[2014:(1+2+3+4)]+...++[2014:(1+2+3+...+2013)]
1) 1/2 + 1/3 + 1/4 + ... + 1/2013 + 1/2014
2) 2014 + 2013/2 + 2012/3 + 2011/4 + ... + 2/2013 + 1/2014
2014+(2014/1+2)+(2014/1+2+3)+...+(2014/1+2+3+4+5+...+2013)=???.Ai giai duoc vay???
2014+(2014/1+2)+(2014/1+2+3)+...+(2014/1+2+3+...+2013)
=2014*(1+(1/1+2)+(1/1+2+3)+...+( 1/1+2+3+...+2013))
=2014*(1+(1/3)+(1/6)+....+(1/2027091)
=2014*2*((1/+(1/2*3)+(1/3*4).....+(1/2013*2014))
=2014*2*(1/1-1/2+1/2-1/3+1/3-1/4+.....+1/2013-1/2014)
=2014*2*(1-1/2014)
=2*(2014*2013/2014)
=2*2013
=4026
Cuối cùng cũng giải được.
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Cho S=1+2014+2014^2+2014^3+.........+2014^2013.Cho P =2014^2014/2013.Tính P-S
Ta có: \(2014S=2014\left(1+2014+2014^2+2014^3+...+2014^{2013}\right)\)
\(2014S=2014+2014^2+2014^3+2014^4+...+2014^{2014}\)
\(2014S-S=\left(2014+2014^2+2014^3+2014^4+...+2014^{2014}\right)-\left(1+2014+2014^2+2014^3+...+2014^{2013}\right)\)
\(2013S=2014^{2014}-1\)
\(S=\dfrac{2014^{2014}-1}{2013}\)
\(P-S=\dfrac{2014^{2014}}{2013}-\dfrac{2014^{2014}-1}{2013}=\dfrac{1}{2013}\)
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1/1*2+1/3*2+1/5*6+.....+1/2013*2014
-------------------------------------------------------
1/1008*2014+1/1009*2013+1/1010*2012+....1/2014*2018
frac{frac{1}{2}+frac{1}{3}+......+frac{1}{2013}}{frac{2012}{1}+frac{2012}{2}+frac{2011}{3}+...+frac{1}{2013}}frac{frac{1}{2}+frac{1}{3}+..+frac{1}{2013}}{frac{2012}{1}+2+frac{2012}{2}+1+frac{2011}{3}+1+...+frac{1}{2013}+1-2014}frac{frac{1}{2}+frac{1}{3}+...+frac{1}{2013}}{frac{2014}{1}+frac{2014}{2}+...+frac{2014}{2013}-2014}frac{frac{1}{2}+frac{1}{3}+...+frac{1}{2013}}{2014left(1+frac{1}{2}+frac{1}{3}+...+frac{1}{2013}-1right)}frac{1}{2014}
Đọc tiếp
\(\frac{\frac{1}{2}+\frac{1}{3}+......+\frac{1}{2013}}{\frac{2012}{1}+\frac{2012}{2}+\frac{2011}{3}+...+\frac{1}{2013}}\)
=\(\frac{\frac{1}{2}+\frac{1}{3}+..+\frac{1}{2013}}{\frac{2012}{1}+2+\frac{2012}{2}+1+\frac{2011}{3}+1+...+\frac{1}{2013}+1-2014}\)
=\(\frac{\frac{1}{2}+\frac{1}{3}+...+\frac{1}{2013}}{\frac{2014}{1}+\frac{2014}{2}+...+\frac{2014}{2013}-2014}\)
=\(\frac{\frac{1}{2}+\frac{1}{3}+...+\frac{1}{2013}}{2014\left(1+\frac{1}{2}+\frac{1}{3}+...+\frac{1}{2013}-1\right)}\)
=\(\frac{1}{2014}\)
Tính:
(2014/1+2014/2+2013/3+...+2/2014+1/2015)/(3/2015+3/2014+...+3/2)
Tính:
A= 2014 + \(\frac{2014}{1+2}+\frac{2014}{1+2+3}+\frac{2014}{1+2+3+4}+........+\frac{2014}{1+2+3+4+.....+2013}\)
\(A=2014.\left(1+\frac{1}{1+2}+\frac{1}{1+2+3}+...+\frac{1}{1+2+3+...+2013}\right)\)
\(A=2014.\left(1+\frac{1}{3}+\frac{1}{6}+...+\frac{1}{1007.2013}\right)\)
\(A=2.2014.\left(\frac{1}{2}+\frac{1}{6}+\frac{1}{12}+...+\frac{1}{2013.2014}\right)\)
\(A=2.2014.\left(\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+...+\frac{1}{2013.2014}\right)\)
\(A=2.2014.\left(1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{2013}-\frac{1}{2014}\right)\)
\(A=2.2014.\left(1-\frac{1}{2014}\right)\)
\(A=2.2014.\frac{2013}{2014}\)
\(A=\frac{2.2014.2013}{2014}\)
\(A=2.2013\)
\(A=4026\)
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