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

zin cho cách giải lun nha bạn crityamo the anh

A =............=  867

đề sai sao làm được????????????????

làm rồi

2/5

tick nha

= 1/(3x5) + 1/(5x7) + 1/(7x9) +.....+ 1/(99x101)                                                                                                 =( 1/3 -1/5 + 1/5 -1/7 +1/7 - 1/9 +....+ 1/99 -1/101 ) :2                                                                                        = (1/3 -1/101) : 2                                                                                                                                           = 98/303 : 2                                                                                                                                                   = 49/303

tick cai nao cho dung

=1/3*5+1/5*7+1/7*9+...+1/99*101

=1/3-1/5+1/5-1/7+...+1/99-1/101

=1/3-1/101

=98/303

1/15 + 1/35 + 1/63 + 1/99 + ... + 1/9999 

= 1/(3x5) + 1/(5x7) + 1/(7x9) + ... + 1/(99x101)

= (1/3 - 1/5 + 1/5 - 1/7 + 1/7 - 1/9 + ...+ 1/99 - 1/101) : 2

= (1/3 - 1/101) : 2 

= 98/303 : 2

= 49/303

\(a=\frac{1}{15}+\frac{1}{35}+\frac{1}{63}+....+\frac{1}{9999}\)

\(a=\frac{1}{3.5}+\frac{1}{5.7}+\frac{1}{7.9}+....+\frac{1}{99.101}\)

\(a=\frac{1}{2}.\left(\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-....-\frac{1}{101}\right)\)

\(a=\frac{1}{2}.\left(\frac{1}{3}-\frac{1}{101}\right)=\frac{49}{303}\)

Đặt \(B=\frac{3}{15}+\frac{3}{35}+\frac{3}{63}+\frac{3}{99}+\frac{3}{143}\)

\(\Leftrightarrow B=\frac{3}{3.5}+\frac{3}{5.7}+\frac{3}{7.9}+\frac{3}{9.11}+\frac{3}{11.13}\)

\(\Leftrightarrow2B=3\left(\frac{2}{3.5}+\frac{2}{5.7}+\frac{2}{7.9}+\frac{2}{9.11}+\frac{2}{11.13}\right)\)

\(\Leftrightarrow2B=3\left(\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+\frac{1}{7}-\frac{1}{9}+\frac{1}{9}-\frac{1}{11}+\frac{1}{11}-\frac{1}{13}\right)\)

\(\Leftrightarrow2B=3\left(\frac{1}{3}-\frac{1}{13}\right)=1-\frac{3}{13}=\frac{10}{13}\)

\(\Leftrightarrow A=1+\frac{3}{15}+\frac{3}{35}+\frac{3}{63}+\frac{3}{99}+\frac{3}{143}=1+\frac{10}{13}=\frac{23}{13}\)

1/3 + 1/15 + 1/35 + 1/63 + 1/99 + 9999

= 1/3 + ( 1/5 + 1/35 + 1/63 ) + 1/99 = 9999

= 1/3 + 1111/9999 + 1/99

= 3333/9999 + 1111/9999 +101/9999

= 4545/9999

4546/9999

có thể giải hẳn ra được ko cái này tính máy tính cũng ra

\(\frac{2}{3}+\frac{2}{15}+\frac{2}{35}+\frac{2}{63}+\frac{2}{99}\)

\(=\frac{2}{1.3}+\frac{2}{3.5}+\frac{2}{5.7}+\frac{2}{7.9}+\frac{2}{9.11}\)

\(=1-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+\frac{1}{7}-\frac{1}{9}+\frac{1}{9}-\frac{1}{11}\)

\(=1-\frac{1}{11}\)

\(=\frac{10}{11}\)

\(\frac{1}{2}+\frac{1}{6}+\frac{1}{12}+\frac{1}{20}+\frac{1}{30}+\frac{1}{42}\)

\(=\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+\frac{1}{4.5}+\frac{1}{5.6}+\frac{1}{6.7}\)

\(=1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+\frac{1}{5}-\frac{1}{6}+\frac{1}{6}-\frac{1}{7}\)

\(=1-\frac{1}{7}\)

\(=\frac{6}{7}\)

\(\frac{2}{3}+\frac{2}{15}+\frac{2}{35}+\frac{2}{63}+\frac{2}{99}\)

\(=\frac{2}{1.3}+\frac{2}{3.5}+\frac{2}{5.7}+\frac{2}{7.9}+\frac{2}{9.11}\)

\(=1-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+\frac{1}{7}-\frac{1}{9}+\frac{1}{9}-\frac{1}{11}\)

\(=1-\frac{1}{11}\)

\(=\frac{10}{11}\)

\(\frac{1}{2}+\frac{1}{6}+\frac{1}{12}+\frac{1}{20}+\frac{1}{30}+\frac{1}{42}\)

\(=\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+\frac{1}{4.5}+\frac{1}{5.6}+\frac{1}{6.7}\)

\(=1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+\frac{1}{5}-\frac{1}{6}+\frac{1}{6}-\frac{1}{7}\)

\(=1-\frac{1}{7}\)

\(=\frac{6}{7}\)

A = 1/15 + 1/35 + 1/63 + 1/99 + ....... + 1/9999

A = 1/3 x 5 + 1/5 x 7 + 1/9 x7 + .........+ 1/99 x101

A = 1/2 x ( 1/3 -1/5 + 1/5 - 1/7 + 1/7 - 1/9 + ...... + 1/99 - 1/101

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

A = 1/2 x 98/303

A = 49/303

A = 1/3.5 +1/5.7 + 1/7.9 + 1/9.11 + ... + 1/99. 101

= 1/2.(2/3.5+ 2/5.7 + 2/7.9 + ...+2/99.101)

= 1/2.(1/3 - 1/5 - 1/5 - 1/7 - 1/7 - 1/9  + .... +1/99 - 1/101

=1/2.(1/3 - 1/101)

=1/2 .98//303

=49/303

Dấu . là nhân đó nha bạn