Ta có:

A= 1/1.3 + 1/3.5 + .....+ 1/5.7 +......+ 1/19.21

2.A = 2/1.3 + 2/3.5 + 2/5.7 +...+ 2/19.21

2.A=  1- 1/3+ 1/3- 1/5+ 1/5- 1/7+............+ 1/19 - 1/21

2.A= 1- 1/21

2.A = 20/21

A= 20/21 : 2

A = 10/21

=> D

=>A mk nhầm

A=\(\dfrac{2}{1.3}-\dfrac{2}{3.5}-\dfrac{2}{5.7}-.....-\dfrac{2}{23.25}-\dfrac{1}{27}\)

A=\(\dfrac{2}{3}-\left(\dfrac{2}{3.5}+\dfrac{2}{5.7}+....+\dfrac{2}{23.25}\right)-\dfrac{1}{27}\)

A=\(\dfrac{2}{3}-\left(\dfrac{1}{3}-\dfrac{1}{5}+\dfrac{1}{5}-\dfrac{1}{7}+......+\dfrac{1}{23}-\dfrac{1}{25}\right)-\dfrac{1}{27}\)

A=\(\dfrac{2}{3}-\left(\dfrac{1}{3}-\dfrac{1}{25}\right)-\dfrac{1}{27}\)

A=\(\dfrac{2}{3}-\dfrac{22}{75}-\dfrac{1}{27}\)

A=\(\dfrac{227}{675}\)

\(\frac{1}{1\cdot3}+\frac{1}{3\cdot5}+\frac{1}{5\cdot7}+...+\frac{1}{19\cdot21}-\frac{x}{14}=\frac{2}{-7}\)

\(\frac{1}{2}\left(\frac{2}{1\cdot3}+\frac{2}{3\cdot5}+\frac{2}{5\cdot7}+...+\frac{2}{19\cdot21}\right)-\frac{x}{14}=\frac{2}{-7}\)

\(\frac{1}{2}\left(1-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+...+\frac{1}{19}-\frac{1}{21}\right)-\frac{x}{14}=\frac{2}{-7}\)

\(\frac{1}{2}\left(1-\frac{1}{21}\right)-\frac{x}{14}=\frac{2}{-7}\)

\(\frac{1}{2}\cdot\frac{20}{21}-\frac{x}{14}=\frac{2}{-7}\)

\(\frac{10}{21}-\frac{x}{14}=\frac{2}{-7}\)

\(\frac{x}{14}=\frac{10}{21}-\frac{2}{-7}\)

\(\frac{x}{14}=\frac{16}{21}\)

\(\Rightarrow x\cdot=21=14\cdot16\)

\(\Rightarrow x\cdot21=224\)

\(\Rightarrow x=\frac{224}{21}\)

\(A=-\left(\frac{2}{1.3}+\frac{2}{3.5}+\frac{2}{5.7}+...+\frac{2}{25.27}\right)-\frac{1}{27}\)

\(=-\left(1-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+...+\frac{1}{25}-\frac{1}{27}\right)-\frac{1}{27}\)

\(=-\left(1-\frac{1}{27}\right)-\frac{1}{27}\)

\(=-1+\frac{1}{27}-\frac{1}{27}\)

\(=-1\)

1/2015

\(A=-\left(\frac{2}{1.3}+\frac{2}{3.5}+\frac{2}{5.7}+...+\frac{2}{25.27}\right)-\frac{1}{27}\)

   \(=-\left(1-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+...+\frac{1}{25}-\frac{1}{27}\right)-\frac{1}{27}\)

    \(=-\left(1-\frac{1}{27}\right)-\frac{1}{27}\)

    \(=-1+\frac{1}{27}-\frac{1}{27}\)

     \(=-1\)

sao làm như vậy được??? 2/19.21 và 2/23.25 bn k làm được như thế đâu vì nó k cùng quy luật với các ps kia

S= 1/1.3 + 1/3.5 + 1/5.7 +................+ 1/200.202

=>S=1/2.(2/1.3+2/3.5+2/5.7+...+2/200.202)

=>S=1/2.(3-1/1.3+5-3/3.5+...+202-200/200.202)

=>S=1/2.(1-1/3+1/3-1/5+...+1/200-1/202)

=>S=1/2.(1-1/202)

=>S=1/2.201/202

=>S=201/404

Vậy S=201/404

\(2.S=\frac{2}{1.3}+\frac{2}{3.5}+\frac{2}{5.7}+...+\frac{2}{2017.2019}\)

\(=\frac{3-1}{1.3}+\frac{5-3}{3.5}+\frac{7-5}{5.7}+...+\frac{2019-2017}{2017.2019}\)

\(=1-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+...+\frac{1}{2017}-\frac{1}{2019}\)

\(=1-\frac{1}{2019}=\frac{2018}{2019}\)

=> \(S=\frac{1009}{2019}\)

Tính: S= 1/1.3 + 1/3.5 +1/5.7 + 1009/2019 .....+ 1/2017.2019

Trả lời:

1009/2019