gọi biểu thức tên là A , ta có :

A= (1/21+1/210+1/2010). ( 1/3-1/30-1/5-1/10)

A = (1/21+1/210+1/2010) . 0

A = 0

  Công Chúa Giá Băng    làm đúng nhất !

tổng trên sẽ là:

1/1+1/3+1/210=3/321

đáp số:3/321

=14\15.20\21....209\210

=14.2\15.2.20.2\21.2....209.2\210.2

=4.7\5.6.5.8\6.7.....19.20\20.21

=4.5.6....19\5.6.7...20.7.8.9....22\6.7.8.....21

=4\20.22\6

=1\5-11\3

=11\15

k cho mik nha

Có chắc ko đó bạn

Lời giải:

$\frac{A}{2}=\frac{1}{2}-\frac{1}{6}-\frac{1}{12}-\frac{1}{20}-...-\frac{1}{420}$

$\frac{A}{2}=\frac{1}{2}-\left(\frac{1}{6}+\frac{1}{12}+\frac{1}{20}+...+\frac{1}{420}\right)$

Xét:

$\frac{1}{6}+\frac{1}{12}+\frac{1}{20}+...+\frac{1}{420}=\frac{1}{2.3}+\frac{1}{3.4}+\frac{1}{4.5}+...+\frac{1}{20.21}$

$=\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+...+\frac{1}{20}-\frac{1}{21}$

$=\frac{1}{2}-\frac{1}{21}$

Do đó:

$\frac{A}{2}=\frac{1}{2}-(\frac{1}{2}-\frac{1}{21})=\frac{1}{21}$

$\Rightarrow A=\frac{2}{21}$

Ta có:\(\frac{1}{42}+\frac{1}{56}+\frac{1}{72}+...+\frac{1}{210}\) 

   \(=\frac{1}{6.7}+\frac{1}{7.8}+\frac{1}{8.9}+....+\frac{1}{14.15}\)

    \(=\frac{1}{6}-\frac{1}{7}+\frac{1}{7}-\frac{1}{8}+...+\frac{1}{14}-\frac{1}{15}\)

      \(=\frac{1}{6}-\frac{1}{15}=\frac{1}{10}\)

C = \(\left(1-\frac{1}{3}\right)\left(1-\frac{1}{6}\right)\left(1-\frac{1}{10}\right)...\left(1-\frac{1}{210}\right)=\frac{2}{3}.\frac{5}{6}.\frac{9}{10}...\frac{209}{210}=\frac{4}{6}.\frac{10}{12}.\frac{18}{20}...\frac{418}{420}\)

= \(\frac{2.2}{2.3}.\frac{2.5}{3.4}.\frac{3.6}{4.5}...\frac{19.22}{20.21}=\frac{2.2\left(2.3.4...19\right)\left(5.6...22\right)}{\left(2.3.4..20\right)\left(3.4.5..21\right)}=\frac{4.22}{19.3.4}=\frac{22}{57}\)