\(\frac{1}{10}+\frac{1}{30}+\frac{1}{60}+\frac{1}{100}+\frac{1}{150}\)

= \(\frac{1}{10}.\left(1+\frac{1}{3}+\frac{1}{6}+\frac{1}{10}+\frac{1}{15}\right)\)

= \(\frac{1}{10}.2.\left(\frac{1}{2}+\frac{1}{6}+\frac{1}{12}+\frac{1}{20}+\frac{1}{30}\right)\)

= \(\frac{1}{5}.\left(\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+\frac{1}{4.5}+\frac{1}{5.6}\right)\)

= \(\frac{1}{5}.\left(1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+\frac{1}{5}-\frac{1}{6}\right)\)

= \(\frac{1}{5}.\left(1-\frac{1}{6}\right)\)

= \(\frac{1}{5}.\frac{5}{6}\)

= \(\frac{1}{6}\)

\(\frac{1}{10}+\frac{1}{30}+\frac{1}{60}+\frac{1}{100}+\frac{1}{150}\)

\(=\frac{1}{10}.\left(1+\frac{1}{3}+\frac{1}{6}+\frac{1}{10}+\frac{1}{15}\right)\)

\(=\frac{1}{10}.2.\left(\frac{1}{2}+\frac{1}{6}+\frac{1}{12}+\frac{1}{20}+\frac{1}{30}\right)\)

\(=\frac{1}{10}.2.\left(\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+\frac{1}{4.5}+\frac{1}{5.6}\right)\)

\(=\frac{1}{10}.2.\left(1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+\frac{1}{5}-\frac{1}{6}\right)\)

\(=\frac{1}{5}.\left(1-\frac{1}{6}\right)\)

\(=\frac{1}{5}.\frac{5}{6}\)

\(=\frac{1}{6}\)

Rất vui vì giúp đc bạn <3

\(\frac{1}{10}+\frac{1}{30}+\frac{1}{60}+\frac{1}{100}+\frac{1}{150}\)

\(=\frac{1}{10}.\left(1+\frac{1}{3}+\frac{1}{6}+\frac{1}{10}+\frac{1}{15}\right)\)

\(=\frac{1}{10}.\left(\frac{30}{30}+\frac{10}{30}+\frac{5}{30}+\frac{3}{30}+\frac{2}{30}\right)\)

\(=\frac{1}{10}.\frac{5}{3}\)

\(=\frac{1}{2}.\frac{1}{3}\)

\(=\frac{1}{6}\)

đặt 1/6 chung rồi giải 

A = \(\frac{2}{3}\). \(\frac{5}{6}\). \(\frac{9}{10}\).\(\frac{14}{15}\)... \(\frac{209}{210}\)

  = \(\frac{4}{6}\). \(\frac{10}{12}\).\(\frac{18}{20}\).\(\frac{28}{30}\)... \(\frac{418}{420}\)

  = \(\frac{4.10.18.28...418}{6.12.20.30...420}\)

  =  \(\frac{1.4.2.5.3.6.4.7...19.22}{2.3.3.4.4.5.5.6...20.21}\)

  = \(\frac{\left(1.2.3.4...19\right)\left(4.5.6.7...22\right)}{\left(2.3.4.5...20\right)\left(3.4.5.6...21\right)}\)

  =  \(\frac{1.22}{20.3}\)= \(\frac{22}{60}\)= \(\frac{11}{30}\)

=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

\(S=1+\frac{1}{2}+\frac{2}{2}+\frac{3}{2}+\frac{4}{2}+...+\frac{101}{2}\)

\(S=1+\frac{1+2+3+4+...+101}{2}\)

\(S=1+\frac{10201}{2}=...\)

tick cho mink nha!

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

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

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

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

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 !