\(\frac{\frac{1}{2012}+\frac{1}{2013}-\frac{1}{2014}}{\frac{5}{2012}+\frac{5}{2013}-\frac{5}{2014}}-\frac{\frac{2}{2013}+\frac{2}{2014}-\frac{2}{2015}}{\frac{3}{2013}+\frac{3}{2014}-\frac{3}{2015}}\)

=\(\frac{\frac{1}{2012}+\frac{1}{2013}-\frac{1}{2014}}{5\left(\frac{1}{2012}+\frac{1}{2013}-\frac{1}{2014}\right)}-\frac{2\left(\frac{1}{2013}+\frac{1}{2014}-\frac{1}{2015}\right)}{3\left(\frac{1}{2013}+\frac{1}{2014}-\frac{1}{2015}\right)}=\frac{1}{5}-\frac{2}{3}=\frac{3}{15}-\frac{10}{15}=-\frac{7}{15}\)

biết vậy mà vẫn đòi lấy ảnh! ok!

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.

Ta có: \(2014S=2014\left(1+2014+2014^2+2014^3+...+2014^{2013}\right)\)

\(2014S=2014+2014^2+2014^3+2014^4+...+2014^{2014}\)

\(2014S-S=\left(2014+2014^2+2014^3+2014^4+...+2014^{2014}\right)-\left(1+2014+2014^2+2014^3+...+2014^{2013}\right)\)

\(2013S=2014^{2014}-1\)

\(S=\dfrac{2014^{2014}-1}{2013}\)

\(P-S=\dfrac{2014^{2014}}{2013}-\dfrac{2014^{2014}-1}{2013}=\dfrac{1}{2013}\)

cảm ơn bạn

Bạn hỏi hay trả lời luôn dzậy?

\(A=2014.\left(1+\frac{1}{1+2}+\frac{1}{1+2+3}+...+\frac{1}{1+2+3+...+2013}\right)\)

\(A=2014.\left(1+\frac{1}{3}+\frac{1}{6}+...+\frac{1}{1007.2013}\right)\)

\(A=2.2014.\left(\frac{1}{2}+\frac{1}{6}+\frac{1}{12}+...+\frac{1}{2013.2014}\right)\)

\(A=2.2014.\left(\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+...+\frac{1}{2013.2014}\right)\)

\(A=2.2014.\left(1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{2013}-\frac{1}{2014}\right)\)

\(A=2.2014.\left(1-\frac{1}{2014}\right)\)

\(A=2.2014.\frac{2013}{2014}\)

\(A=\frac{2.2014.2013}{2014}\)

\(A=2.2013\)

\(A=4026\)

A=4026