M=2/3.5+2/5.7+/.............+2/97/99

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

=1/3-1/99

=32/99

OK

xin 5 tích vì mất 5 phút

Giải:

\(B=\dfrac{3}{3\times5}+\dfrac{3}{5\times7}+\dfrac{3}{7\times9}+...+\dfrac{3}{48\times50}\) 

\(B=\dfrac{3}{2}\times\left(\dfrac{2}{3\times5}+\dfrac{2}{5\times7}+\dfrac{2}{7\times9}+...+\dfrac{2}{48\times50}\right)\) 

\(B=\dfrac{3}{2}\times\left(\dfrac{1}{3}-\dfrac{1}{5}+\dfrac{1}{5}-\dfrac{1}{7}+\dfrac{1}{7}-\dfrac{1}{9}+...+\dfrac{1}{48}-\dfrac{1}{50}\right)\) 

\(B=\dfrac{3}{2}\times\left(\dfrac{1}{3}-\dfrac{1}{50}\right)\)

\(B=\dfrac{3}{2}\times\dfrac{47}{150}\) 

\(B=\dfrac{47}{100}\) 

Chúc em học tốt!

917749738461936926399639748776398646491639394748947630373937366

\(\left(\frac{1}{1.3}+\frac{1}{3.5}+\frac{1}{5.7}+\frac{1}{7.9}+\frac{1}{9.11}\right)y=\frac{2}{3}\)

=> \(\frac{1}{2}\left(1-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+\frac{1}{7}-\frac{1}{9}+\frac{1}{9}-\frac{1}{11}\right)y=\frac{2}{3}\)

=> \(\frac{1}{2}\left(1-\frac{1}{11}\right)y=\frac{2}{3}\)

=> \(\frac{1}{2}.\frac{10}{11}y=\frac{2}{3}\)

=> \(\frac{5}{11}y=\frac{2}{3}\)

=>y = \(\frac{2}{3}:\frac{5}{11}\)

=> y = \(\frac{22}{15}\)

cho mk cái lời giải thích chỗ nhân 1/2 ý mk ko hiểu mong bn thông cảm

bạn phạm khánh hà ơi dấu chấm ở giữa các phân số có nghĩa là dấu nhân đó

\(2.\left(\frac{2}{1.3}+\frac{2}{3.5}+\frac{2}{5.7}+\frac{2}{7.9}+\frac{2}{9.11}\right).y=\frac{2}{3}\)

\(2\left(\frac{1}{1}-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+...+\frac{1}{9}-\frac{1}{11}\right).y=\frac{2}{3}\)

\(2.\left(\frac{1}{1}-\frac{1}{11}\right).y=\frac{2}{3}\)

\(2.\frac{10}{11}.y=\frac{2}{3}\)

\(\frac{20}{11}.y=\frac{2}{3}\)

\(\Rightarrow y=\frac{11}{30}\)

Study well 

Đặt \(A=\frac{3}{5.7}+\frac{3}{7.9}+....+\frac{3}{59.61}\)

 \(\Rightarrow\frac{2}{3}.A=\frac{2}{3}.\left(\frac{3}{5.7}+\frac{3}{7.9}+....+\frac{3}{59.61}\right)\)

\(\Rightarrow\frac{2}{3}.A=\frac{2}{5.7}+\frac{2}{7.9}+....+\frac{2}{59.61}\)

\(\Rightarrow\frac{2}{3}.A=\frac{7-5}{5.7}+\frac{9-7}{7.9}+.....+\frac{61-59}{59.61}\)

\(\Rightarrow\frac{2}{3}.A=\frac{1}{5}-\frac{1}{7}+\frac{1}{7}-\frac{1}{9}+....+\frac{1}{59}-\frac{1}{61}\)

\(\Rightarrow\frac{2}{3}.A=\frac{1}{5}-\frac{1}{61}\)

\(\Rightarrow\frac{2}{3}.A=\frac{56}{305}\)

\(\Rightarrow A=\frac{56}{305}:\frac{2}{3}\)

\(\Rightarrow A=\frac{56}{305}.\frac{3}{2}\)

\(\Rightarrow A=\frac{84}{305}\)

Vậy \(\frac{3}{5.7}+\frac{3}{7.9}+....+\frac{3}{59.61}=\frac{84}{305}\)

\((\frac{1}{1\cdot3}+\frac{1}{3\cdot5}+\frac{1}{5\cdot7}+\frac{1}{7\cdot9}+\frac{1}{9\cdot11})\cdot y=\frac{2}{3}\)

\(\Rightarrow(1-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+\frac{1}{7}-\frac{1}{9}+\frac{1}{9}-\frac{1}{11}+\frac{1}{11})\cdot y=\frac{2}{3}\)

\(\Rightarrow1-\frac{1}{11}\cdot y=\frac{2}{3}\)

\(\Rightarrow\frac{10}{11}\cdot y=\frac{2}{3}\)

\(\Rightarrow y=\frac{2}{3}:\frac{10}{11}=\frac{11}{15}\)

Vậy :\(y=\frac{11}{15}\)

Bạn có muốn mình thử lại không?

không cảm ơn bạn

quá dễ :

A=3/3x5+3/5x7+3/7x9+...+3/97x99

A=3/2.(1/3-1/5+1/5-1/3+...+1/97-1/99)

A=3/2.(1/3-1/99)

A=3/2.32/99

A= 16/33 

A = 3/3x5 + 3/5x7 + 3/7x9 + ... + 3/97x99

A = 3/2 . (1/3 - 1/5 + 1/5 - 1/3 + ... + 1/97 - 1/99)

A = 3/2 . (1/3 - 1/99)

A = 3/2 . 32/99

A = 16/33