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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

C=1/(2x4)+1/(4x6)+...+1/(18x20)

2C=2/(2x4)+2/(4x6)+...+2/(18x20)

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

2C= 1/2- 1/20

2C= 9/20

C= 9/20 x 1/2

C= 9/40

- Quên k auto súc vặc

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

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

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

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

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

\(9-x=0\)

\(x=9-0\)

\(x=9\)

\(\frac{4}{2\cdot4}+\frac{4}{4\cdot6}+...+\frac{4}{16\cdot18}\)

\(=2\cdot\left(\frac{2}{2\cdot4}+\frac{2}{4\cdot6}+...+\frac{2}{16\cdot18}\right)\)

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

\(=2\cdot\left(\frac{1}{2}-\frac{1}{18}\right)\)

\(=2\cdot\frac{4}{9}\)

\(=\frac{8}{9}\)

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