\(A=\frac{3-1}{1.3}+\frac{5-3}{3.5}+...+\frac{101-99}{99.101}\)

\(A=1-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+...+\frac{1}{99}-\frac{1}{101}=\frac{100}{101}\)

\(=2.\left(\frac{1}{1.3}+\frac{1}{3.5}+..+\frac{1}{9.11}\right)\)

\(=2.\left(1-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+...-\frac{1}{11}\right)\)

\(=2.\left(1-\frac{1}{11}\right)\)

\(=2.\left(\frac{11}{11}-\frac{1}{11}\right)\)

\(=2.\frac{10}{11}\)

\(=\frac{20}{11}\)

Lời giải:
$2\times A=\frac{2}{1\times 3}+\frac{2}{3\times 5}+\frac{2}{5\times 7}+...+\frac{2}{19\times 21}$
$2\times A=\frac{3-1}{1\times 3}+\frac{5-3}{3\times 5}+\frac{7-5}{5\times 7}+...+\frac{21-19}{19\times 21}$

$=1-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+....+\frac{1}{19}-\frac{1}{21}$

$=1-\frac{1}{21}=\frac{20}{21}$

$\Rightarrow A=\frac{20}{21}: 2= \frac{10}{21}$

14,26651106

=7/8.8/3.9/5.5

=7/3.9

=21

`7/8xx9/5xx8/3xx5=[7xx3xx3xx8xx5]/[8xx5xx3]=7xx3=21`

\(=\dfrac{7\times3\times3\times8\times5}{8\times5\times3}=\dfrac{21}{1}=21\)

= 2/ 1x3 +2/ 3x5 +2/ 5x7 + 2/ 7 x9+............+2/2011 x 2003 +2 / 2003 x 2005

\(\left(x\cdot2,4-4,2\right)\div x=1\)

\(\Rightarrow x\cdot2,4-4,2=x\)

\(\Rightarrow x\cdot2,4=x+4,2\)

\(\Rightarrow\frac{12x}{5}=\frac{5x+21}{5}\)

\(\Rightarrow12x=5x+21\)

\(\Rightarrow12x-5x=21\)

\(\Rightarrow7x=21\Rightarrow x=\frac{21}{7}=3\)

Vậy x = 3 

\(\frac{1}{1\cdot3}+\frac{1}{3\cdot5}+...+\frac{1}{x\left(x+2\right)}\)

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

\(=\frac{1}{2}\cdot\left(1-\frac{1}{x+2}\right)\)

\(=\frac{1}{2}\cdot\frac{x+1}{x+2}\)

\(=\frac{x+1}{2x+2}\)

Đề sai bn ơi :  Sửa : \(\frac{\frac{7}{3}+\frac{7}{4}-\frac{7}{11}}{\frac{5}{3}+\frac{5}{4}-\frac{5}{11}}+\frac{5}{7}\)

\(=\frac{7\cdot\left(\frac{1}{3}+\frac{1}{4}-\frac{1}{11}\right)}{5\cdot\left(\frac{1}{3}+\frac{1}{4}-\frac{1}{11}\right)}+\frac{5}{7}\)

\(=\frac{7}{5}+\frac{5}{7}=\frac{49}{35}+\frac{25}{35}=\frac{74}{35}\)

1/2 x (6/1-6/3+6/3-6/5+ ... +6/37-6/39)

1/2 x (6/1-6/39)

1/2 x 228/39

228/78

\(\frac{6}{1\cdot3}+\frac{6}{3.5}+\frac{6}{5.7}+...+\frac{6}{35.37}+\frac{6}{37.39}\) 

\(=3\left(1-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+...+\frac{1}{37}-\frac{1}{39}\right)\) 

\(=3\left(1-\frac{1}{39}\right)=3\cdot\frac{38}{39}=\frac{114}{39}\) 

Ps: Bạn tự rút gọn nhé!!!

\(\frac{6}{1.3}+\frac{6}{3.5}+...+\frac{6}{35.37}+\frac{6}{37.39}\)

\(=3\left(\frac{2}{1.3}+\frac{2}{3.5}+...+\frac{2}{35.37}+\frac{2}{37.39}\right)\)

\(=3\left(\frac{1}{1}-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+...+\frac{1}{37}-\frac{1}{39}\right)\)

\(=3\left(1-\frac{1}{39}\right)\)

\(=3.\frac{38}{39}\)

\(=\frac{38}{13}\)

a ) A = 20,15 x 25,75 + 74,25 x 20,15

     A = 20,15 x ( 25,75 + 74,25 )

     A = 20,15 x       100

     A =     2015

Tính bằng cách thuận tiện nhất 

a) A = 20,15 x 25,75 + 74,25 x 20,15

= 20,15 x (25,75 + 74,25)

= 20,15 x      100

= 2015

 b ) B = 2/1x3 + 2/3x5 + 2/5x7 + 2/7x9 + 2/9x7

      B = 1 - 1/3 + 1/3 - 1/5 + 1/5 - 1/7 + 1/7 - 1/9

       B =  1 + ( 1/3 - 1/3 ) + ( 1/5 - 1/5 ) + ( 1/7 - 1/7 ) - 1/9

       B =  1 - 1/9

       B =   8/9

bạn có thể tìm kiếm , có nhiều người hỏi phàn B lắm