Question

[Nguyễn Thị Quỳnh Lê]

A=\(\frac{1}{4}+\frac{1}{12}+\frac{1}{36}+\frac{1}{108}+\frac{1}{324}+\frac{1}{972}\)

Answer 1

[Ahwi]

\(A=\frac{1}{4}+\frac{1}{12}+\frac{1}{36}+\frac{1}{108}+\frac{1}{324}+\frac{1}{972}.\)

\(3A=3\left(\frac{1}{4}+\frac{1}{12}+\frac{1}{36}+\frac{1}{108}+\frac{1}{324}+\frac{1}{972}\right).\)

\(3A=\frac{3}{4}+\frac{3}{12}+\frac{3}{36}+\frac{3}{108}+\frac{3}{324}+\frac{3}{972}\)

\(3A=\frac{3}{4}+\frac{1}{4}+\frac{1}{12}+\frac{1}{36}+\frac{1}{108}+\frac{1}{324}\)

\(2A=\frac{3}{4}+\frac{1}{4}+\frac{1}{12}+\frac{1}{36}+\frac{1}{108}+\frac{1}{324}-\frac{1}{4}-\frac{1}{12}-\frac{1}{36}-\frac{1}{108}-\frac{1}{324}-\frac{1}{972}\)

\(2A=\frac{3}{4}-\frac{1}{972}=\frac{182}{243}\)

\(\Rightarrow A=\frac{182}{243}:2=\frac{91}{243}\)

\(\Rightarrow A=\frac{1}{4}+\frac{1}{12}+\frac{1}{36}+\frac{1}{108}+\frac{1}{324}+\frac{1}{972}=\frac{91}{243}\)

Answer 2

[Trần Hữu Hoàng]

ta có    

A x 3 =3/4 + 3/12 + 3/36 +3/108 + 3/324 +3/972

A x 3=3/4 +1/4 + 1/12 +1/36 +1/108

A x 3 - A =(3/4 +1/12+1/36 +1/108)-(1/4 +1/12 +1/36 +1/108 +1/324 + 1/972)

A x 2=3/4 +1/12 +1/36 +1/108 - 1/4 -1/12 -1/36-1/108 -1/324 -1/972

A x 2= 3/4 - 1/972

A x 2= 728/972

A =728/972 : 2

A=91/243