đặt A=1/18+1/54+1/108+...+1/990
\(A=\frac{1}{3.6}+\frac{1}{6.9}+\frac{1}{9.12}+...+\frac{1}{30.33}\)
\(=\frac{1}{3}\times\left(\frac{3}{3.6}+\frac{3}{6.9}+...+\frac{3}{30.33}\right)\)
\(=\frac{1}{3}\times\left(\frac{1}{3}-\frac{1}{6}+\frac{1}{6}-\frac{1}{9}+...+\frac{1}{30}-\frac{1}{33}\right)\)
\(=\frac{1}{3}\times\left(\frac{1}{3}-\frac{1}{33}\right)\)
\(=\frac{1}{3}\times\frac{10}{33}\)
\(=\frac{10}{99}\)
1/18 + 1/54 + ..... + 1/990
= 1/3.6 +1/6.9 +...... + 1/30.33
= 1/3 . ( 1/3 - 1/6 + 1/6 - 1/9 + ..... + 1/30 -1/33 )
= 1/3 . ( 1/3 - 1/33 )
= 1/3 . 10/33
= 10/99
