Question

\(\frac{1}{18}+\frac{1}{54}+\frac{1}{108}+....+\frac{1}{990}\)

Answer 1

\(\frac{1}{18}\)+ \(\frac{1}{54}\)+ \(\frac{1}{108}\)+ ... + \(\frac{1}{990}\)

=\(\frac{1}{3}\).(3.( \(\frac{1}{3.6}\) + \(\frac{1}{6.9}\) + \(\frac{1}{9.12}\) + ... + \(\frac{1}{30.33}\) ))

= \(\frac{1}{3}\). (\(\frac{3}{3.6}\) + \(\frac{3}{6.9}\) + \(\frac{3}{9.12}\) + ... + \(\frac{3}{30.33}\) )

= \(\frac{1}{3}\) . ( \(\frac{1}{3}-\frac{1}{6}\) + \(\frac{1}{6}-\frac{1}{9}\) + \(\frac{1}{9}-\frac{1}{12}\) + ... + \(\frac{1}{30}-\frac{1}{33}\) )

=\(\frac{1}{3}\) . ( \(\frac{1}{3}-\frac{1}{33}\) )

= \(\frac{1}{3}\) . \(\frac{10}{33}\)

= \(\frac{10}{99}\)

Nhớ k cho mình nhé!!!

Answer 2

     \(\frac{1}{18}+\frac{1}{54}+\frac{1}{108}+....+\frac{1}{990}\)

\(=\frac{1}{3.6}+\frac{1}{6.9}+\frac{1}{9.12}+.....+\frac{1}{30.33}\)

\(=\frac{1}{3}.\left(\frac{1}{3}-\frac{1}{6}+\frac{1}{6}-\frac{1}{9}+\frac{1}{9}-\frac{1}{12}+.....+\frac{1}{30}-\frac{1}{33}\right)\)

\(=\frac{1}{3}.\left(\frac{1}{3}-\frac{1}{33}\right)\)

\(=\frac{1}{3}.\left(\frac{11}{33}-\frac{1}{33}\right)\)

\(=\frac{1}{3}.\frac{10}{33}\)

\(=\frac{10}{99}\)

Answer 3

\(=\frac{1}{3\times6}+\frac{1}{6\times9}+...+\)\(\frac{1}{30\times33}\)

=\(\frac{1}{3}\times\)( \(\frac{1}{3}-\frac{1}{6}+\frac{1}{6}-\frac{1}{9}+....+\frac{1}{30}-\frac{1}{33}\))

=\(\frac{1}{3}\times\)(\(\frac{1}{3}-\frac{1}{33}\))

=\(\frac{1}{3}\times\frac{10}{33}\)=\(\frac{10}{99}\)