1/15 +1/35 +1/63 + 1/99 +...+1/2915 +1/3135

=1/3x5+1/5x7+1/7x9+....+1/53x55+1/55x57

=1/3-1/5+1/5-1/7+1/7-1/9+.....+1/53-1/55+1/55-1/57

=1/3-1/57

=6/19 nhé

Ta có:1/15+1/35+1/63+1/99+...+1/2915+1/3135=1/3*5+1/5*7+1/7*9+1/9*11+...+1/53*55+1/55*57

=1/3-1/5+1/5-1/7+1/7-1/9+1/9-1/11+...+1/53-1/55+1/55-1/57

=1/3-1/57=19/57-1/57=18/57

\(\frac{1}{15}+\frac{1}{35}+\frac{1}{63}+..+\frac{1}{3135}\)\(=\frac{1}{3.5}+\frac{1}{5.7}+\frac{1}{7.9}+..+\frac{1}{55.57}\)
\(\Rightarrow\)\(\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+\frac{1}{7}-\frac{1}{9}\)\(+...+\frac{1}{55}-\frac{1}{57}\)\(=\frac{1}{3}-\frac{1}{57}=\frac{6}{19}\)

 

Tổng các số đó là:

\(\dfrac{1}{3}+\dfrac{1}{15}+\dfrac{1}{35}+\dfrac{1}{63}+...+\dfrac{1}{399}\)

\(=\dfrac{1}{1\times3}+\dfrac{1}{3\times5}+\dfrac{1}{5\times7}+\dfrac{1}{7\times9}+...+\dfrac{1}{19\times21}\)

\(=\dfrac{1}{2}\times\left(\dfrac{2}{1\times3}+\dfrac{2}{3\times5}+\dfrac{2}{5\times7}+\dfrac{2}{7\times9}+...+\dfrac{2}{19\times21}\right)\)

\(=\dfrac{1}{2}\times\left(1-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{5}+\dfrac{1}{5}-\dfrac{1}{7}+\dfrac{1}{7}-\dfrac{1}{9}+...+\dfrac{1}{19}-\dfrac{1}{21}\right)\)

\(=\dfrac{1}{2}\times\left(1-\dfrac{1}{21}\right)\)

\(=\dfrac{1}{2}\times\dfrac{20}{21}\)

\(=\dfrac{10}{21}\)

A = \(\dfrac{1}{3}\) + \(\dfrac{1}{15}\) + \(\dfrac{1}{35}\) + \(\dfrac{1}{63}\) +...+

A = \(\dfrac{1}{1.3}\) + \(\dfrac{1}{3.5}\)+ \(\dfrac{1}{5.7}\) + \(\dfrac{1}{7.9}\)+...+

Xét dãy số 1; 3; 5; 7;...; Đây là dãy số cách đều với khoảng cách là

        3 - 1 = 2

Số thứ 10 của dãy số trên là 2 x (10 - 1) + 1  = 19

Vậy tổng của mười phân số đầu tiên của tổng A là:

         A = \(\dfrac{1}{1.3}\) + \(\dfrac{1}{3.5}\) + \(\dfrac{1}{5.7}\) + \(\dfrac{1}{7.9}\) +....+ \(\dfrac{1}{19.21}\)

         A = \(\dfrac{2}{2}\).(\(\dfrac{1}{1.3}\) + \(\dfrac{1}{3.5}\) + \(\dfrac{1}{5.7}\) + \(\dfrac{1}{7.9}\) +...+ \(\dfrac{1}{19.21}\)

        A = \(\dfrac{1}{2}\).(\(\dfrac{2}{1.3}\) + \(\dfrac{2}{3.5}\) + \(\dfrac{2}{5.7}\) + \(\dfrac{2}{7.9}\)+...+ \(\dfrac{2}{19.21}\))

       A = \(\dfrac{1}{2}\). (\(\dfrac{1}{1}\) - \(\dfrac{1}{3}\) + \(\dfrac{1}{3}\) - \(\dfrac{1}{5}\) + \(\dfrac{1}{5}\) - \(\dfrac{1}{7}\) + ...+ \(\dfrac{1}{19}\) - \(\dfrac{1}{21}\)

       A = \(\dfrac{1}{2}\).( \(\dfrac{1}{1}\) - \(\dfrac{1}{21}\))

      A = \(\dfrac{1}{2}\). \(\dfrac{20}{21}\)

      A = \(\dfrac{10}{21}\)

\(A=\frac{1}{1.3}+\frac{1}{3.5}+\frac{1}{5.7}+\frac{1}{7.9}+...+\frac{1}{11.13}\)

\(A=1-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+...+\frac{1}{11}-\frac{1}{13}\)

\(A=1-\frac{1}{13}\)

\(A=\frac{12}{13}\)

A = 1/3 + 1/15 + 1/35 + 1/63 +.....+ 1/143

   = 1/1.3 + 1/3.5 + 1/5.7 + 1/7.9 +.....+1/11.13

   = 1/2 . (1 - 1/3 + 1/3 - 1/5 + 1/5 - 1/7 + 1/7 - 1/9 +...+ 1/11 - 1/13)

   = 1/2 . (1 - 1/13)

   = 1/2 . 12/13

   = 6/13

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

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

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

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

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

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

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

cám ơi bạn

cảm ơn bạn rất nhiều

            A=12/15 + 28/315

            A=8/9 

Đặt \(A=\)\(\frac{1}{15}+\frac{1}{35}+...+\frac{1}{143}\)

\(=\frac{1}{3.5}+\frac{1}{5.7}+...+\frac{1}{11.13}\)

\(2A=\frac{2}{3.5}+\frac{2}{5.7}+...+\frac{2}{11.13}\)

\(2A=\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+...+\frac{1}{11}-\frac{1}{13}\)

\(2A=\frac{1}{3}-\frac{1}{13}=\frac{10}{39}\)

\(A=\frac{5}{39}\)

Câu còn lại cx dựa như vậy nhé bn ! 

Chúc bn hc tốt <3

câu c hình như sai đề hả bn

2a= 2/3+2/8+2/15+2/24+2/35+2/48+2/63+2/80= [2/( 1*3)+2/( 3*5)+2/( 5*7)+2/( 7*9)]+[2/(2*4)+2/(4*6)+2/(6*8)+2/(8*10)]= [1/1-1/3+1/3-1/5+1/5-1/7+1/7-1/9]+[1/2-1/4+1/4-1/6+1/6-1/8+1/8-1/10]= [1/1-1/9]+[1/2-1/10]= 8/9+2/5= 58/45 =>a= 29/45

A=1/1.3 + 1/3.5 + 1/5.7 + 1/7.9 + 1/9.11 + 1/11.13 + 1/13.15

A=1/1 - 1/3 +1/3 - 1/5 +1/5 -1/7+......+1/13 - 1/15

A=1 - 1/15

A=1/14

bạn ơi: 

1/195 mới bằng 1/13.15 mà!!

1/3+1/15+1/35+1/63+1/99+1/143+1/180=1/1.3+1/3.5+1/5.7+1/7.9+1/9.11+1/11.13+1/13.15

=1/2.(1-1/3+1/3-1/5+1/5-1/7+1/7-1/9+.....+1/13-1/15)

=1/2.(1-1/15)

=1/2.14/15

=7/15

chúc học tốt