Bạn hỏi hay trả lời luôn dzậy?

Ta có : 1 + 2 + 3 + ... + n = \(\frac{\left(n+1\right)n}{2}\)

Vậy nên : \(A=2013+\frac{2013}{\frac{3.2}{2}}+\frac{2013}{\frac{4.3}{2}}+...+\frac{2013}{\frac{2013.2012}{2}}\)

\(A=2013+\frac{4026}{2.3}+\frac{4016}{3.4}+...+\frac{4026}{2012.2013}\)

\(A=4026\left(\frac{1}{1.2}+\frac{1}{2.3}+...+\frac{1}{2012.2013}\right)\)

\(A=4026\left(1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+...+\frac{1}{2012}-\frac{1}{2013}\right)\)

\(A=4026\left(1-\frac{1}{2013}\right)=4026.\frac{2012}{2013}=4024.\)

\(D=\frac{\frac{2013}{2}+\frac{2013}{3}+\frac{2013}{4}+...+\frac{2013}{2014}}{\frac{2013}{1}+\frac{2012}{2}+\frac{2011}{3}+...+\frac{1}{2013}}\)

\(=\frac{2013\left(\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+...+\frac{1}{2014}\right)}{\left(\frac{2012}{2}+1\right)+\left(\frac{2011}{3}+1\right)+...+\left(\frac{1}{2013}+1\right)+1}\)

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

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

\(=\frac{2013}{2014}\)

2013/2014

\(\frac{2013}{2014}\)

óc chó      c hó

B=2013.(1+

\(\frac{1}{1+2}+\frac{1}{1+2+3}+\frac{1}{1+2+3+4}+...+\frac{2013}{1+2+3+...+2012}\)

B=2013(\(\frac{2}{1.2}+\frac{2}{2.3}+\frac{2}{3.4}+\frac{2}{4.5}+...+\frac{2}{2012.2013}\)

B=2013.2(\(1\frac{1}{2013}=2013.2.\frac{2012}{2013}=4024\)

Maỳ có bị óc chó không mà bảo câu trả lời của đại ca tao là sai

A=\(\frac{2013}{2014}\) nha

Mình nghĩ kết quả là: 2013/2014

tk mình nhé

Chúc bạn học tốt

Mình đang cần

^.^

2013/2014.

\(C=\frac{2013\left(\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+....+\frac{1}{2014}\right)}{\frac{2012}{2}+1+\frac{2011}{3}+1+......+\frac{1}{2013}+1+1}=\frac{2013.\left(\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+\frac{..........1}{2014}\right)}{\frac{2014}{2}+\frac{2014}{3}+.......+\frac{2014}{2013}+\frac{2014}{2014}}\)

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