`1/15+1/35+1/63+1/99+1/143`

`=1/[3.5]+1/[5.7]+1/[7.9]+1/[9.11]+1/[11.13]`

`=1/2(2/[3.5]+2/[5.7]+2/[7.9]+2/[9.11]+2/[11.13])`

`=1/2.(1/3-1/5+1/5-1/7+...+1/11-1/13)`

`=1/2.(1/3-1/13)`

`=1/2 . 10/39`

`=5/39`

\(\frac{1}{15}+\frac{1}{35}+\frac{1}{63}+\frac{1}{99}+\frac{1}{143}+\frac{1}{195}\)

\(=\frac{1}{2}\cdot\left(\frac{2}{3\cdot5}+\frac{2}{5\cdot7}+\frac{2}{7\cdot9}+\frac{2}{9\cdot11}+\frac{2}{11\cdot13}+\frac{2}{13\cdot15}\right)\)

\(=\frac{1}{2}\cdot\left(\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+\frac{1}{7}-\frac{1}{9}+\frac{1}{9}-\frac{1}{11}+\frac{1}{11}-\frac{1}{13}+\frac{1}{13}-\frac{1}{15}\right)\)

\(=\frac{1}{2}\cdot\left(\frac{1}{3}-\frac{1}{15}\right)=\frac{1}{2}\cdot\frac{4}{15}=\frac{2}{15}\)

\(\dfrac{1}{3}+\dfrac{1}{15}+\dfrac{1}{25}+\dfrac{1}{35}+\dfrac{1}{63}+\dfrac{1}{99}+\dfrac{1}{143}\)

\(=\left(\dfrac{2}{1\cdot3}+\dfrac{2}{3\cdot5}+\dfrac{2}{5\cdot7}+\dfrac{2}{7\cdot9}+\dfrac{2}{9\cdot11}+\dfrac{2}{11\cdot13}\right)\cdot\dfrac{1}{2}+\dfrac{1}{25}\)

\(=\left(1-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{5}+\dfrac{1}{5}-\dfrac{1}{7}+\dfrac{1}{7}-...+\dfrac{1}{11}-\dfrac{1}{13}\right)\cdot\dfrac{1}{2}+\dfrac{1}{25}\)

\(=\left(1-\dfrac{1}{3}\right)\cdot\dfrac{1}{2}+\dfrac{1}{25}\)

\(=\dfrac{2}{3}\cdot\dfrac{1}{2}+\dfrac{1}{25}\)

\(=\dfrac{1}{3}+\dfrac{1}{25}\)

\(=\dfrac{28}{75}\)

cám ơi bạn

cảm ơn bạn rất nhiều

ta có

(1/3+1/6+1/36) +(1/10+1/15+1/45)+(1/21+1/28)

=(\(\frac{12+6+1}{36}\)+\(\frac{9+6+2}{90}\)+\(\frac{4+3}{84}\)

19/36+17/90+1/12

=(19/36+1/12)+17/90

=7/12+17/90

=105/180+34/180

=139/180

1/3 +1/6+1/10+1/15+1/21+1/28+1/36+1/45

=1/1x3+1/3x2+1/2x5+1/3x5+1/3x7+1/7x4+1/4x9+1/9x5

=1/1-1/3+1/3-1/2....+1/9-1/5

=1/1

bạn ơ sao mình tính trong máy tính đc 4/5 mà

=\(\frac{1}{3\cdot5}+\frac{1}{5.7}+\frac{1}{7.9}+...+\frac{1}{11\cdot13}=\frac{1}{2}\left(\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+...+\frac{1}{11}-\frac{1}{13}\right)\)

\(=\frac{1}{2}\left(\frac{1}{3}-\frac{1}{13}\right)=\frac{1}{2}.\frac{10}{13}=\frac{5}{13}\) 

B=1/15+1/35+1/63+1/99+1/143

B=1/3.5+1/5.7+1/7.9+1/9.11+11.13    (khoảng cách từ 3-5;5-7;7-9;9-11;11-13 la 2)

Suy ra B=1/2(1/3-1/5+1/5-1/7+1/7-1/9+1/9-1/11+1/11-1/13) (Ta gop -1/5+1/5;-1/7+1/7;-1/9+1/9;-1/11+1/11 bang 0)

B=1/2(1/3-1/43)=1/2.40/129=20/129

tk đi rồi mk tk lại......

A=1/3.5+1/5.7+1/7.9+1/9.11+1/11.13

A=1/2 [1/3-1/5+1/5-1/7+1/7-1/9+1/9-1/11+1/11-1/13]

A=1/2.10/39

A=5/39

ai tk mình

mình tk lại

=5/39

 tk mk đi mk tk cho hứa đó

A=1/15+1/35+1/63+1/99+1/143+1/195+1/255+1/323

=> A = 1/3.5 + 1/5.7 + 1/7.9 + 1/9.11 + 1/11.13 + 1/13.15 + 1/15.17 + 1/17.19

=> 2A = 1/3 - 1/5 + 1/5 - 1/7 + ..... + 1/17 - 1/19

=> 2A = 1/3 - 1/19

=> 2A = 16/57 => A = 16/57 : 2 = 8/57

=>=> A = 1/3.5 + 1/5.7 + 1/7.9 + 1/9.11 + 1/11.13 + 1/13.15 + 1/15.17 + 1/17.19

=>=> 2A = 1/3 - 1/5 + 1/5 - 1/7 + ..... + 1/17 - 1/19

=> 2A = 1/3 - 1/19

=> 2A = 16/57 => A = 16/57 : 2 = 8/57

1/15+1/35+1/63+1/99+1/143+1/195+1/255+1/323

=1/3-1/5+1/5-1/7+1/7-1/9+1/9-1/11+1/11-1/13+1/13-1/15+1/15-1/17+1/17-1/19

=2/3-2/5+2/5-2/7+2/7-2/9+2/9-2/11+2/11-2/13+2/13-2/15+2/15-2/17+2/17-2/19

=1/3-1/19

2/9

Giải: 
Đặt A = 1/3+1/15+1/35+1/63+1/99+1/143+1/195 
2A= 2/(1.3) + 2/(3.5) + 2/(5.7) + 2/(7.9)+2/(9.11) + 2/(11.13)+2/(13.15) 
2A=1/1-1/3+1/3-1/5+1/5-1/7+1/7-1/9+1/9... 
2A=1/1-1/15=14/15 
Vậy A=14/15 : 2 = 7/15

Nhấn đúng mk nha             Tran Dan 

  \(\frac{1}{3}+\frac{1}{15}+\frac{1}{35}+..+\frac{1}{143}+\frac{1}{195}\)

=\(\frac{1}{1.3}+\frac{1}{3.5}+\frac{1}{5.7}+..+\frac{1}{13.15}\)

= \(\frac{1}{1}-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+..+\frac{1}{13}-\frac{1}{15}\)

= \(1-\frac{1}{15}=\frac{14}{15}\)

tick đúng nha 

A = \(\frac{1}{1\times3}+\frac{1}{3\times5}+\frac{1}{5\times7}+...+\frac{1}{13\times15}=\frac{1}{2}\times\left(\frac{2}{1\times3}+\frac{2}{3\times5}+\frac{2}{5\times7}+...+\frac{2}{13\times15}\right)\)

A = \(\frac{1}{2}\times\left(\frac{1}{1}-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+...+\frac{1}{13}-\frac{1}{15}\right)=\frac{1}{2}\times\left(1-\frac{1}{15}\right)=\frac{7}{15}\)