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

\(=\frac{1}{3\times6}+\frac{1}{6\times9}+\frac{1}{9\times11}+....+\frac{1}{30\times30}\)

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

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

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

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

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

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

\(=\frac{1}{3}\left(\frac{1}{3}-\frac{1}{33}\right)=\frac{1}{3}.\frac{10}{33}=\frac{10}{99}\)

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

\(=\frac{1}{3\cdot6}+\frac{1}{6\cdot9}+\frac{1}{9\cdot12}+...+\frac{1}{30\cdot33}\)

\(=\frac{1}{3}\left(\frac{3}{3\cdot6}+\frac{3}{6\cdot9}+\frac{3}{9\cdot12}+...+\frac{3}{30\cdot33}\right)\)

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

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

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

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

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

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

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

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

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

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

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

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

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

\(=\frac{1}{3}\left(\frac{1}{3}-\frac{1}{33}\right)=\frac{10}{99}\)

1/6*3+1/6*9+1/9*12+........+1/30*33

=(1/3-1/6)+(1/6-1/9)+(1/9-1/12)+........+(1/30-1/33)

=1/3-1/6+1/6-1/9+1/9-1/12+........+1/30-1/33

=1/3-1/33

=10/33

nho k cho mink nha 

CHUC BAN HOC GIOI !

Gợi ý: 18 = 3.6

           54 = 6.9

           108 = 9.12

           .............

           990 = 30.33

Gấp 3 lần R rồi dùng sai phân hữu hạn.

Tự làm tiếp nhé!!!

đặt A với biểu thức trên

A=\(\frac{1}{3x6}\)+\(\frac{1}{6x9}\)+......+\(\frac{1}{30x33}\)

Nhân cả 2 vế với 3 ta có

A x 3 = \(\frac{3}{3x6}\)+....+\(\frac{3}{30x33}\)

A x 3 = \(\frac{1}{3}\)-\(\frac{1}{6}\)+....+\(\frac{1}{30}\)-\(\frac{1}{33}\)

A x 3 = \(\frac{1}{3}\)-\(\frac{1}{33}\)

A x 3 = \(\frac{10}{33}\)

A = \(\frac{10}{33}\):3

A= \(\frac{10}{99}\)

cho vài k đi bà con ơi

a = 10 | 99 nhé

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

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

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

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

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

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

1/18+1/54+1/108+...+1/990

=1/3 x 6+1/6 x 9+1/9 x 12+...+1/30 x 33

=(1/3-1/6)+(1/6-1/9)+...+1(/30-1/33)

=1/3-1/6+1/6-1/9+...+1/30-1/33

=1/3-1/33

=10/33

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

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

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

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

\(F=\frac{11}{33}-\frac{1}{33}\)

\(F=\frac{10}{33}\)

Chúc bạn học tốt !!!! 

 f =1/18+1/54+1/108+...+1/990

F=1/3.6+1/6.9+1/9.12+...+1/30.33

F=3/3.6+3/6.9+3/9.12+...+3/30.33

F=1/3-1/6+1/6-1/9+...+1/30-1/33

F=1/3-1/33

F=11/33-1/33

F=10/33

Vậy F=10/33.

dấu chấm là dấu nhân nha bạn

chúc bạn học tốt ^^. cho mình nha

                                                 giải

1/18 + 1/54 +1/108 + ......+ 1/990

ta tách mẫu số ra thành 1 tích của 2 số :

1/3x6 + 1/6x9 + 1/9x12 +........ + 1/30x33

theo quy tắc ta có : nếu tử nhân với 3 thì mẩu cũng sẽ nhân với 3 :

1x3/3x6x3 +1x3/6x9x3 + 1x3/9x11x3 + .........+ 1x3/30x33x3

= 1/3 x  (  3/3x6 + 3/6x9 + 3/9x11 +.....+3/30x33

= 1/3 x ( 1/3 - 1/33 )

= 1/3 x 10/33

=10/99

Mình giải hơi khó hiểu 1 chút nha

1/18+1/54+1/108+...+1/990

=1/3*6+1/6*9+1/9*12+...+1/30*33\

=(1/3-1/6)+(1/6-1/9)+...+1(/30-1/33)

=1/3-1/6+1/6-1/9+...+1/30-1/33

=1/3-1/33

=10/33