A bn lướt xuống dưới mà xem cách làm 

nhưng của bn là cho 3 ra ngoài nha

Giải:

A=3/1.3+3/3.5+3/5.7+...+3/49.51

A=3/2.(2/1.3+2/3.5+2/5.7+...+2/49.51)

A=3/2.(1/1-1/3+1/3-1/5+1/5-1/7+...+1/49-1/51)

A=3/2.(1/1-1/51)

A=3/2.50/51

A=25/17

B=1/3+1/3²+1/3³+...+1/3⁸

3B=1+1/3+1/3²+...+1/3⁷

3B-B=(1+1/3+1/3²+...+1/3⁷)-(1/3+1/3²+1/3³+...+1/3⁸)

2B=1-1/3⁸

   B=1-1/3⁸ /2

Chúc bạn học tốt!

Hướng dẫn:

\(M=\frac{1^2}{1.3}+\frac{2^2}{3.5}+\frac{3^2}{5.7}+...+\frac{99^2}{197.199}\)

\(\Rightarrow4M=\frac{1.4}{1.3}+\frac{4.4}{3.5}+\frac{9.4}{5.7}+...+\frac{9801.4}{197.199}\)

\(\Rightarrow4M=\frac{2.2}{1.3}+\frac{4.4}{3.5}+\frac{6.6}{5.7}+...+\frac{198.198}{197.199}\)

Đến đoạn này bạn đưa về dạng tổng quát nhé:

\(\frac{n^2}{\left(2n-1\right)\left(2n+1\right)}=\frac{1}{4}+\frac{1}{8\left(2n-1\right)}-\frac{1}{8\left(2n+1\right)}\) (Tự phân tích)

Sau đó thay vào A. Kết quả tìm được là \(A=\frac{1}{8}-\frac{1}{8.2013}+\frac{1006}{4}=251,6249379\)

                           \(\frac{3}{1.3}+\frac{3}{3.5}+\frac{3}{5.7}+...+\frac{3}{49.51}\)

                 \(=\frac{2}{3}.\left(\frac{2}{1.3}+\frac{2}{3.5}+\frac{2}{5.7}+...+\frac{2}{49.51}\right)\)

                  \(=\frac{2}{3}.\left(1-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+...+\frac{1}{49}-\frac{1}{51}\right)\)

                   \(=\frac{2}{3}.\left(1-\frac{1}{51}\right)\)

                  \(=\frac{2}{3}.\frac{50}{51}=\frac{20}{51}\)

              Ủng hộ mk nha !!! ^_^

25/17 mới đúng

\(\frac{3}{1.3}\)+ \(\frac{3}{3.5}\)+ \(\frac{3}{5.7}\)+...+ \(\frac{3}{49.51}\)

= \(\frac{3}{2}\)( \(\frac{2}{1.3}\)+ \(\frac{2}{3.5}\)+ \(\frac{2}{5.7}\)+...+ \(\frac{2}{49.51}\))

= \(\frac{3}{2}\)( \(\frac{1}{1}\)- \(\frac{1}{3}\)+ \(\frac{1}{3}\)- \(\frac{1}{5}\)+ \(\frac{1}{5}\)- \(\frac{1}{7}\)+...+ \(\frac{1}{49}\)- \(\frac{1}{51}\))

= \(\frac{3}{2}\)( 1- \(\frac{1}{51}\))

= \(\frac{3}{2}\). \(\frac{50}{51}\)

= \(\frac{25}{17}\).

= 1 - 1/3 + 1/3 - 1/5 + 1/5 - 1/7 +....... + 1/97 - 1/99

= 1- 1/99

= 98/99

Mãi yêu chàng trai Song Tử:bạn làm vầy là ngu roày

3/1.3+3/3.5+3/5.7+....+3/97.99=98/99

3/1.3 + 3/3.5 + 3/5.7 + ....... + 3/49.51

= 3 x ( 1/1.3 + 1/3.5 + 1/5.7 + .... + 1/49.51 )

= 3 x ( 1 - 1/51 )

= 3 x      50/51

=       150/151

\(A=\frac{3}{1.3}+\frac{3}{3.5}+\frac{3}{5.7}+...+\frac{3}{49.51}\)

\(A=\frac{3}{2}\left(\frac{2}{1.3}+\frac{2}{3.5}+\frac{2}{5.7}+...+\frac{2}{49.51}\right)\)

 
\(A=\frac{3}{2}\left(1-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+...+\frac{1}{49}-\frac{1}{51}\right)\)

\(A=\frac{3}{2}\left(1-\frac{1}{51}\right)\)

\(A=\frac{3}{2}.\frac{50}{51}=\frac{25}{17}\)

1/1-1/3+1/3-1/5+1/5-1/7+...... +1/47-1/49

 3/1.3+3/3.5+3/5.7+......+3/47.49

=1/1-1/3+1/3-1/5+1/5-1/7+........+1/47-1/49

=1/1-1/49

=49/49-1/49

=48/49

= 1 - 1/3 + 1/3 - 1/5 + 1/5 - 1/7 +......+ 1/47 - 1/49

= 1 - 1/49

= 48/49 nha!

*** Ai k mk mk k lại !!***

Mọi người giúp mình với

\(\frac{3}{1.3}+\frac{3}{3.5}+...+\frac{3}{49.51}\)

\(=\frac{3}{2}.\left(\frac{2}{1.3}+\frac{2}{3.5}+...+\frac{2}{49.51}\right)\)

\(=\frac{3}{2}.\left(1-\frac{1}{51}\right)\)

\(=\frac{25}{17}\)

Xin lỗi em mới học dạng này hả để anh làm lại cho hiểu nhé

 \(\frac{3}{1.3}+\frac{3}{3.5}+...+\frac{3}{49.51}\)

\(=\frac{3}{2}.\left(\frac{2}{1.3}+\frac{2}{3.5}+...+\frac{2}{49.51}\right)\)

\(=\frac{3}{2}.\left(1-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+...+\frac{1}{49}-\frac{1}{51}\right)\)

\(=\frac{3}{2}.\left(1-\frac{1}{51}\right)\)

\(=\frac{3}{2}.\frac{50}{51}\)

\(=\frac{25}{17}\)

Nhanh lên mình đang cần gấp lắm 

Gấp lắm hả :V

\(A=\frac{3}{1\cdot3}+\frac{3}{3\cdot5}+\frac{3}{5\cdot7}+....+\frac{3}{2001\cdot2003}\)

\(=\frac{3}{2}\left(\frac{1}{1}-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+.....+\frac{1}{2001}-\frac{1}{2003}\right)\)

\(=\frac{3}{2}\left(1-\frac{1}{2003}\right)=\frac{6006}{4006}\)