Ta gọi biểu thức đó là A

Ta có công thức        \(\frac{a}{b.c}=\frac{a}{c-b}.\left(\frac{1}{b}-\frac{1}{c}\right)\)

Dựa vào công thức ta có  

\(\frac{4}{2.4}=2.\left(\frac{1}{2}-\frac{1}{4}\right)\)

\(\frac{4}{4.6}=2.\left(\frac{1}{4}-\frac{1}{6}\right)\)

\(....................\)

\(\frac{4}{18.20}=2.\left(\frac{1}{18}-\frac{1}{20}\right)\)

\(\Rightarrow\)\(A=2.\left(\frac{1}{2}-\frac{1}{4}+\frac{1}{4}-\frac{1}{6}+....+\frac{1}{18}-\frac{1}{20}\right)\)

\(\Rightarrow\)\(A=2.\left(\frac{1}{2}-\frac{1}{20}\right)\)

\(\Rightarrow\)\(A=2.\left(\frac{9}{20}\right)=\frac{18}{20}\)

Ai thấy đúng thì ủng hộ nha !!!

sai rồi kết quả phải bằng 9/10 chứ 

\(\frac{4}{2\cdot4}+\frac{4}{4\cdot6}+\frac{4}{6\cdot8}+...+\frac{4}{18\cdot20}\)

\(=2\left(\frac{2}{2\cdot4}+\frac{2}{4\cdot6}+\frac{2}{6\cdot8}+...+\frac{2}{18\cdot20}\right)\)

\(=2\left(\frac{1}{2}-\frac{1}{4}+\frac{1}{4}-\frac{1}{6}+\frac{1}{6}-\frac{1}{8}+...+\frac{1}{18}-\frac{1}{20}\right)\)

\(=2\left(\frac{1}{2}-\frac{1}{20}\right)\)

\(=2\left(\frac{9}{20}\right)\)\(=\frac{18}{20}=\frac{9}{10}\)

ax4=1/2-1/4+1/4-1/6+1/6+1/8+.......+1/16-1/18+1/18+1/20

ax4  =1/2-1/20

 ax4 =9/20

   a=9/20:4

   a=9/80

THANKS

\(a,\frac{4}{2.4}+\frac{4}{4.6}+\frac{4}{6.8}+....+\frac{4}{16.18}+\frac{4}{18.20}\)

\(=\frac{4}{2}\left(\frac{1}{2}-\frac{1}{4}+\frac{1}{4}-\frac{1}{6}+\frac{1}{6}-\frac{1}{8}+...+\frac{1}{18}-\frac{1}{20}\right)\)

\(=2\left(\frac{1}{2}-\frac{1}{20}\right)\)

\(=2.\frac{9}{20}\)

\(=\frac{9}{10}\)

\(b,\frac{1}{2}+\frac{1}{6}+\frac{1}{12}+...+\frac{1}{90}\)

\(=\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+...+\frac{1}{9.10}\)

\(=1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{9}-\frac{1}{10}\)

\(=1-\frac{1}{10}\)

\(=\frac{9}{10}\)

thank you

a, \(\frac{4}{2.4}+\frac{4}{4.6}+\frac{4}{6.8}+..+\frac{4}{16.18}+\frac{4}{18.20}\)

\(=\frac{4}{2}\cdot\left(\frac{1}{2}-\frac{1}{4}+\frac{1}{4}-\frac{1}{6}+....+\frac{1}{16}-\frac{1}{18}+\frac{1}{18}-\frac{1}{20}\right)\)

\(=2\cdot\left(\frac{1}{2}-\frac{1}{20}\right)\)

\(=2\cdot\frac{9}{20}=\frac{9}{10}\)

b, \(\frac{1}{2}+\frac{1}{6}+\frac{1}{12}+\frac{1}{20}+...+\frac{1}{90}\)

\(=\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+...+\frac{1}{9.10}\)

\(=1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+...+\frac{1}{9}-\frac{1}{10}\)

\(=1-\frac{1}{10}=\frac{9}{10}\)

2/2×4 + 2/4×6 + ... + 2/16×18 + 2/18×20

= 1/2 - 1/4 + 1/4 - 1/6 + ... + 1/16 - 1/18 + 1/18 - 1/20

= 1/2 - 1/20

= 10/20 - 9/20

= 9/20

2/2x4+2/4x6+...+2/16x18+2/18x20

=1/2=1/4+1/4-1/6+...+1/16-1/18+1/18-1/20

=1/2-1/20

=10/20-9/20

=1/20

2/2x4 + 2/4x6 + .....+ 2/16x18 + 2/18x20

=1/2-1/4+1/4-1/6+...+1/18-1/20

=1/2-1/20

=9/20

\(\left(\frac{1}{2.4}+\frac{1}{4.6}+\frac{1}{6.8}+...+\frac{1}{18.20}\right).10-x=0\)

\(2\left(\frac{2}{2.4}+\frac{2}{4.6}+\frac{2}{6.8}+...+\frac{2}{18.20}\right).10-x=0\)

\(2\left(\frac{1}{2}-\frac{1}{4}+\frac{1}{4}-\frac{1}{6}+\frac{1}{6}-\frac{1}{8}+...+\frac{1}{18}-\frac{1}{20}\right).10-x=0\)

\(2\left(\frac{1}{2}-\frac{1}{20}\right).10-x=0\)

\(2.\frac{9}{20}.10-x=0\)

\(9-x=0\)

\(x=9-0\)

\(x=9\)

`(2/(2xx4)+2/(4xx6)+2/(6xx8)+2/(8xx10))xxy=1/3`

`=>(1/2-1/4+1/4-1/6+1/6-1/8+1/8-1/10)xxy=1/3`

`=>(1/2-1/10)xxy=1/3`

`=>(5/10-1/10)xxy=1/3`

`=>4/10xxy=1/3`

`=>2/5xxy=1/3`

`=>y=1/3:2/5`

`=>y=1/3xx5/2`

`=>y=5/6`

E=2.(2+2)+4.(2+4)+6.(6+2)+....+98.(98+2).

E=2.2+2.2+2.4+4.4+...+98.98+2.98

E=2.(2+4+6+...+98)+(2.2+4.4+6.6+...+98.98)

E=2.2450+40425.4

E=4900+161700

E=166600

Dấu chấm bằng dấu nhân.

Bạn đúng cho mình đi mình giải thích tại sao :(2.2+4.4+…+98.98)=40425.4

rảnh hả cha nội, người ta hỏi y chứ có hỏi e đâu mà trả lời!

tại sao 2²+4²+6²+...+98²