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\(=\dfrac{1}{99\cdot97}-\dfrac{1}{2}\left(\dfrac{2}{1\cdot3}+\dfrac{2}{3\cdot5}+...+\dfrac{2}{95\cdot97}\right)\)

\(=\dfrac{1}{99\cdot97}-\dfrac{1}{2}\left(1-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{5}+...+\dfrac{1}{95}-\dfrac{1}{97}\right)\)

\(=\dfrac{1}{99\cdot97}-\dfrac{1}{2}\cdot\dfrac{96}{97}=\dfrac{-4751}{9603}\)

9 tháng 10 2021

\(=\dfrac{1}{99}-\left(\dfrac{1}{1\cdot3}+\dfrac{1}{3\cdot5}+...+\dfrac{1}{95\cdot97}+\dfrac{1}{97\cdot99}\right)\\ =\dfrac{1}{99}-\dfrac{1}{2}\left(\dfrac{2}{1\cdot3}+\dfrac{2}{3\cdot5}+...+\dfrac{2}{95\cdot97}+\dfrac{2}{97\cdot99}\right)\\ =\dfrac{1}{99}-\dfrac{1}{2}\left(1-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{5}+...+\dfrac{1}{97}-\dfrac{1}{99}\right)\\ =\dfrac{1}{99}-\dfrac{1}{2}\left(1-\dfrac{1}{99}\right)=\dfrac{1}{99}-\dfrac{1}{2}\cdot\dfrac{98}{99}\\ =\dfrac{1}{99}-\dfrac{49}{99}=-\dfrac{48}{99}=-\dfrac{16}{33}\)

18 tháng 10 2017

\(\frac{1}{99\cdot97}-\frac{1}{97\cdot95}-...-\frac{1}{5\cdot3}-\frac{1}{3\cdot1}\)\(=\frac{1}{99\cdot97}-\left(\frac{1}{97\cdot95}+\frac{1}{95\cdot93}+...+\frac{1}{3\cdot1}\right)\)

\(=\frac{1}{99\cdot97}-2\left(\frac{1}{97}-\frac{1}{95}+\frac{1}{95}-\frac{1}{93}+...+\frac{1}{3}-1\right)\)\(=\frac{1}{99\cdot97}-2\left(\frac{1}{97}-1\right)=\frac{1}{9603}-2\cdot\left(-\frac{96}{97}\right)\)\(\frac{1}{9603}-\frac{-192}{97}\)phần còn lại tự làm

18 tháng 10 2017

chết thiếu dấu =

28 tháng 3 2017

Đặt A=\(\dfrac{1}{99.97}-\dfrac{1}{97.95}-........-\dfrac{1}{5.3}-\dfrac{1}{3.1}\)

=\(\dfrac{1}{99.97}-\left(\dfrac{1}{97.95}+\dfrac{1}{95.93}+......+\dfrac{1}{5.3}+\dfrac{1}{3.1}\right)\)

=\(\dfrac{1}{99.97}-\dfrac{1}{2}\left(\dfrac{1}{95}-\dfrac{1}{97}+\dfrac{1}{93}-\dfrac{1}{95}+.......+\dfrac{1}{3}-\dfrac{1}{5}+1-\dfrac{1}{3}\right)\) =\(\dfrac{1}{99.97}-\dfrac{1}{2}\left(1-\dfrac{1}{97}\right)\)

=\(\dfrac{1}{99.97}-\dfrac{1}{2}.\dfrac{96}{97}\)

=\(\dfrac{1}{99.97}-\dfrac{48}{97}\)

=\(\dfrac{1}{99.97}-\dfrac{48.99}{99.97}\)

=\(\dfrac{-4751}{9603}\)

28 tháng 3 2017

Đặt \(A=\dfrac{1}{99.97}-\dfrac{1}{97.95}-\dfrac{1}{95.93}-...-\dfrac{1}{5.3}-\dfrac{1}{3.1}\\ \Rightarrow 2A= \dfrac{2}{99.97}-\dfrac{2}{97.95}-\dfrac{2}{95.93}-...-\dfrac{2}{5.3}-\dfrac{2}{3.1}\\ \Rightarrow 2A=\dfrac{1}{97}-\dfrac{1}{99}-(\dfrac{1}{95}-\dfrac{1}{97})-(\dfrac{1}{93}-\dfrac{1}{95})-...-(\dfrac{1}{1}-\dfrac{1}{3})\\ \Rightarrow 2A = \dfrac{1}{97}-\dfrac{1}{99}-(\dfrac{1}{95}-\dfrac{1}{97}+\dfrac{1}{93}-\dfrac{1}{95}+...+\dfrac{1}{1}-\dfrac{1}{3})\\ \Rightarrow 2A=\dfrac{1}{97}-\dfrac{1}{99}-1+\dfrac{1}{97}\\ \Rightarrow A\)

14 tháng 8 2023

Đặt: \(A=\dfrac{1}{99}-\dfrac{1}{99\cdot97}-\dfrac{1}{97\cdot95}-....-\dfrac{1}{3\cdot1}\)

\(2A=\dfrac{2}{99}-\dfrac{2}{99\cdot97}-\dfrac{2}{97\cdot95}-...-\dfrac{2}{3\cdot1}\)

\(2A=\dfrac{2}{99}-\left(\dfrac{2}{99\cdot97}+\dfrac{2}{97\cdot95}+...+\dfrac{2}{3\cdot1}\right)\)

\(2A=\dfrac{2}{99}-\left(\dfrac{1}{97}-\dfrac{1}{99}+\dfrac{1}{95}-\dfrac{1}{97}+...+\dfrac{1}{3}-\dfrac{1}{5}+1-\dfrac{1}{3}\right)\)

\(2A=\dfrac{2}{99}-\left(-\dfrac{1}{99}+1\right)\)

\(2A=\dfrac{2}{99}-\dfrac{98}{99}\)

\(2A=-\dfrac{439}{99}\)

\(A=-\dfrac{439}{99}:2\)

\(A=-\dfrac{439}{198}\)

14 tháng 8 2023

1/99 - 1/99.97 - 1/97.95 - ... - 1/3.1

= 1/99 - 1/2.(1/97 - 1/99 + 1/95 - 1/97 + ... + 1 - 1/3)

= 1/99 - 1/2.(1 - 1/99)

= 1/99 - 1/2 . 98/99

= 1/99 - 49/99

= -48/99

4 tháng 4 2020

Ta có : \(\frac{1}{99.97}-\frac{1}{97.95}-...-\frac{1}{5.3}-\frac{1}{3.1}\)

           = \(\frac{1}{99.97}-\left(\frac{1}{97.95}+...+\frac{1}{5.3}+\frac{1}{3.1}\right)\)

            =\(\frac{1}{99.97}-\frac{1}{2}.\left(\frac{1}{95}-\frac{1}{97}+\frac{1}{93}-\frac{1}{95}+...+\frac{1}{3}-\frac{1}{5}+1-\frac{1}{3}\right)\)

          = \(\frac{1}{99.97}-\frac{1}{2}.\left(1-\frac{1}{97}\right)\)

          = \(\frac{1}{99.97}-\frac{1}{2}.\frac{96}{97}\)

          = \(\frac{1}{99.97}-\frac{48}{97}=\frac{1}{99.97}-\frac{48.99}{99.97}=\frac{-4751}{9603}\)

4 tháng 4 2020

      \(\frac{1}{99.97}-\frac{1}{97.95}-\frac{1}{95.93}-...-\frac{1}{5.3}-\frac{1}{3.1}\)

\(=\frac{1}{99.97}-\left(\frac{1}{1.3}+\frac{1}{3.5}+...+\frac{1}{93.95}+\frac{1}{95.97}\right)\)

\(=\frac{1}{99.97}-\frac{1}{2}\left(\frac{2}{1.3}+\frac{2}{3.5}+...+\frac{2}{93.95}+\frac{2}{95.97}\right)\)

\(=\frac{1}{99.97}-\frac{1}{2}\left(1-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+...+\frac{1}{93}-\frac{1}{95}+\frac{1}{95}-\frac{1}{97}\right)\)

\(=\frac{1}{99.97}-\frac{1}{2}\left(1-\frac{1}{97}\right)\)

\(=\frac{1}{99.97}-\frac{1}{2}.\frac{96}{97}\)

\(=\frac{1}{9603}-\frac{48}{97}=\frac{-4751}{9603}\)

20 tháng 9 2023

\(B=\dfrac{1}{99\cdot97}-\dfrac{1}{97\cdot95}-\dfrac{1}{95\cdot93}-...-\dfrac{1}{3\cdot1}\)

\(B=-\left(\dfrac{1}{3\cdot1}+\dfrac{1}{5\cdot3}+...+\dfrac{1}{97\cdot99}\right)\)

\(2B=-\left(\dfrac{2}{3\cdot1}+\dfrac{2}{5\cdot3}+...+\dfrac{2}{99\cdot97}\right)\)

\(2B=-\left(1-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{5}+...+\dfrac{1}{97}-\dfrac{1}{99}\right)\)

\(2B=-\left(1-\dfrac{1}{99}\right)\)

\(2B=-\dfrac{98}{99}\)

\(B=-\dfrac{98}{198}\)

Cậu ơi, \(\dfrac{1}{99\cdot97}\) là dương mà sao lại đưa vào ngoặc âm tất cả vậy nhỉ?

29 tháng 1 2020

Đặt: \(A=\frac{1}{99.97}-\frac{1}{97.95}-\frac{1}{95.93}-...-\frac{1}{5.3}-\frac{1}{3.1}\)

\(=\frac{1}{99.97}-\left(\frac{1}{97.95}+\frac{1}{95.93}+...+\frac{1}{3.1}\right)\)

\(=\frac{1}{2}\left(\frac{1}{97}-\frac{1}{99}\right)-\frac{1}{2}\left(1-\frac{1}{3}+...+\frac{1}{93}-\frac{1}{95}+\frac{1}{95}-\frac{1}{97}\right)\)

\(=\frac{1}{2}\left(\frac{1}{97}-\frac{1}{99}\right)-\frac{1}{2}\left(1-\frac{1}{97}\right)\)

\(=\frac{1}{2}.\frac{1}{97}-\frac{1}{2}.\frac{1}{99}-\frac{1}{2}+\frac{1}{2}.\frac{1}{97}\)

\(=-\frac{4751}{9603}\)

Vậy ....

29 tháng 1 2020

\(\frac{1}{99.97}-\frac{1}{97.95}-...-\frac{1}{5.3}-\frac{1}{3.1}\)

\(=\frac{1}{99.97}-\left(\frac{1}{97.95}+...+\frac{1}{5.3}+\frac{1}{3.1}\right)\)

\(=\frac{1}{99.97}-\left(\frac{1}{1.3}+\frac{1}{3.5}+...+\frac{1}{95.97}\right)\left(1\right).\)

Đặt \(A=\frac{1}{1.3}+\frac{1}{3.5}+...+\frac{1}{95.97}\)

\(\Rightarrow A=\frac{1}{2}.\left(\frac{2}{1.3}+\frac{2}{3.5}+...+\frac{2}{95.97}\right)\)

\(\Rightarrow A=\frac{1}{2}.\left(1-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+...+\frac{1}{95}-\frac{1}{97}\right)\)

\(\Rightarrow A=\frac{1}{2}.\left(1-\frac{1}{97}\right)\)

\(\Rightarrow A=\frac{1}{2}.\frac{96}{97}\)

\(\Rightarrow A=\frac{48}{97}.\)

+ Thay A vào \(\left(1\right)\) ta được:

\(\frac{1}{99.97}-\frac{48}{97}\)

\(=\frac{1}{99.97}-\frac{48.99}{99.97}\)

\(=\frac{1-48.99}{99.97}\)

\(=-\frac{4751}{9603}.\)

Vậy \(\frac{1}{99.97}-\frac{1}{97.95}-\frac{1}{95.93}-...-\frac{1}{5.3}-\frac{1}{3.1}=-\frac{4751}{9603}.\)

Chúc bạn học tốt!

16 tháng 3 2017

rễ thế k cho mình trả lời cho

16 tháng 3 2017

kết quả : ~-0.4