Từ dãy trên ta có:

(\(\frac{3}{2}\)+\(\frac{1}{2}\))+(\(\frac{8}{3}\)+\(\frac{2}{3}\))+......+(\(\frac{2600}{51}\)+\(\frac{1}{51}\))                  < vì không có cách nhập hỗn số nên mình đổi ra phân số >

= 2 + 3 + 4 + 5 + 6 + ..........................+ 51

Từ 2 -> 51 có :( 51 - 2 ) : 1 + 1 = 50 số 

Chia ra : 50 : 2 = 25 cặp 

ta có( 51 + 2 ) x 25 =1325

Vậy tổng trên có kết quả bằng 1325       (tớ chỉ nghĩ thế thôi chứ sai đừng trách nhá.Đùa thôi,đúng đấy )

kq cuối nk =1326 (vừa nhìn nhầm )

=2550 nha (hình như thế) 

nhầm =2601

Đặt \(A=-\frac{1}{3}+\frac{1}{3^2}-\frac{1}{3^3}+...+\frac{1}{3^{50}}-\frac{1}{3^{51}}\)

\(\Rightarrow3A=-1+\frac{1}{3}-\frac{1}{3^2}+...+\frac{1}{3^{49}}-\frac{1}{3^{50}}\)

\(\Rightarrow A+3A=\left(-\frac{1}{3}+\frac{1}{3^2}-...-\frac{1}{3^{51}}\right)+\left(-1+\frac{1}{3}-...-\frac{1}{3^{50}}\right)\)

\(\Leftrightarrow4A=-1-\frac{1}{3^{51}}\)

\(\Leftrightarrow4A=-\frac{3^{51}+1}{3^{51}}\Rightarrow A=-\frac{3^{51}+1}{3^{51}.4}\)

cảm ơn bạn Tuấn Anh nhiều nhé

\(B=-\frac{1}{3}+\frac{1}{3^2}-\frac{1}{3^3}+...-\frac{1}{3^{51}}\)

\(3B=-1+\frac{1}{3}-\frac{1}{3^2}+...-\frac{1}{3^{50}}\)

\(4B=-1-\frac{1}{3^{51}}\)

\(B=\frac{-1-\frac{1}{3^{51}}}{4}\)

\(B=\frac{-1}{3}+\frac{1}{3^2}-\frac{1}{3^3}+...+\frac{1}{3^{50}}-\frac{1}{3^{51}}\)

\(3B=-1+\frac{1}{3}-\frac{1}{3^2}+...+\frac{1}{3^{49}}-\frac{1}{3^{50}}\)

\(3B+B=\left(-1+\frac{1}{3}-...-\frac{1}{3^{50}}\right)+\left(-\frac{1}{3}+\frac{1}{3^2}+...+\frac{1}{3^{50}}-\frac{1}{3^{51}}\right)\)

\(4B=-1-\frac{1}{3^{51}}\)

\(B=\frac{-1-\frac{1}{3^{51}}}{4}\)

hok tốt!!

A = \(\frac{\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+...+\frac{1}{49}+\frac{1}{50}}{\frac{1}{49}+\frac{2}{48}+\frac{3}{47}+...+\frac{48}{2}+\frac{49}{1}}=\frac{\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+...+\frac{1}{49}+\frac{1}{50}}{\left(\frac{1}{49}+1\right)+\left(\frac{2}{48}+1\right)+\left(\frac{3}{47}+1\right)+...+\left(\frac{48}{2}+1\right)+\frac{50}{50}}\)

A = \(\frac{\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+...+\frac{1}{49}+\frac{1}{50}}{\frac{50}{49}+\frac{50}{48}+\frac{50}{47}+...+\frac{50}{2}+\frac{50}{50}}=\frac{\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+...+\frac{1}{49}+\frac{1}{50}}{\left(\frac{1}{49}+\frac{1}{48}+\frac{50}{47}+...+\frac{1}{2}+\frac{1}{50}\right).50}=\frac{1}{50}\)

\(A=\frac{T}{M}\)

\(M=\frac{1}{49}+1+\frac{2}{48}+1+\frac{3}{47}+1+.........+\frac{48}{2}+1+1\)

\(=\frac{50}{49}+\frac{50}{48}+\frac{50}{47}+.........+\frac{50}{2}+1\)

\(=50.\left(\frac{1}{49}+\frac{1}{48}+\frac{1}{47}+......+\frac{1}{2}+\frac{1}{50}\right)=50.T\)

\(A=\frac{T}{50T}=\frac{1}{50}\)