`1/4 +x=5/2xx8/7`

`=> 1/4 + x= 40/14`

`=> 1/4 + x= 20/7`

`=> x= 20/7-1/4`

`=>x=73/28`

1/4 + x = 20/7

x = 20/7 - 1/4 

x = 73/28 

vậy x = 73/28

3+2+2+2.8-1+4.1

=3+2+2+16-1+4

=(3+2+2-1)+(16+4)

=(5+2-1)+20

=(7-1)+20

=6+20

=26

Đặt :

\(A=\frac{1}{3.5}+\frac{1}{5.7}+\frac{1}{7.9}+\frac{1}{9.11}\)

\(\Rightarrow2A=\frac{2}{3.5}+\frac{2}{5.7}+\frac{2}{7.9}+\frac{2}{9.11}\)

\(\Rightarrow2A=\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+\frac{1}{7}-\frac{1}{9}+\frac{1}{9}-\frac{1}{11}\)

\(\Rightarrow2A=\frac{1}{3}-\frac{1}{11}\)

\(\Rightarrow2A=\frac{3}{11}\)

\(\Rightarrow A=\frac{3}{22}\)

1/3 x 5 = 1/3 - 1/5 ;  1/5 x 7 = 1/5 - 1/7 ; làm  tương tự  với số còn lại

Ta được :

1/3 - 1/5 + 1/5 - 1/7 + 1/7 - 1/9 + 1/9 - 1/11

= 1/3 - 1/11

=

    ( 1- \(\dfrac{1}{15}\))x ( 1 - \(\dfrac{1}{16}\))x(1- \(\dfrac{1}{17}\)) x.....x(1- \(\dfrac{1}{100}\))

=  \(\dfrac{14}{15}\) x \(\dfrac{15}{16}\)x \(\dfrac{16}{17}\)x......x\(\dfrac{99}{100}\)

= \(\dfrac{15\times16\times17\times.....\times99}{15\times16\times17\times.....\times99}\) x \(\dfrac{14}{100}\)

=  1 x \(\dfrac{14}{100}\)

= \(\dfrac{7}{50}\)

21\32 nha 

B = 1/3 + 1/6 + 1/12 + 1/24 + 1/48 + 1/96 
 
2B = 2(13+16+112+124+148+196)=23+13+16+112+124+148
 B = 2B - B 
= (23+13+16+112+124+148)−(13+16+112+124+148+196)
= (23+13+16+112+124+148)−13−16−112−124−148−196
= 23−196=21/32

A = 1+ 1+1+ ...+ 1 +(\(\dfrac{1}{2}+\dfrac{1}{6}+\dfrac{1}{12}+...+\dfrac{1}{9900}+\dfrac{1}{10100}\))

=(1+1+1+...+1)+ (\(\dfrac{1}{1x2}+\dfrac{1}{2x3}+\dfrac{1}{3x4}+...+\dfrac{1}{99x100}+\dfrac{1}{100x101}\))

=100 +\(1-\dfrac{1}{101}=100-\dfrac{100}{101}=\dfrac{10000}{101}\)

1+1/2+1+1/6+1+1/12+...+1+1/9900

=1+1/1*2+1+1/2.3+....+1+1/99*100

=100*1+1-1/2+1/2-1/3+1/3-1/4...+1/99-1/100

=100+99/100

=10099/100

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Help Help

=1+1/3-1/4+1/4-1/5+1/5-1/6

=1+1/3-1/6

=1+1/6=7/6