Question

Tính nhanh: 

1+ 1/3 + 1/9 + 1/27 + 1/81 + 1/243 + 1/729

 

Answer 1

1+ 1/3 + 1/9 + 1/27 + 1/81 + 1/243 + 1/729

=1093/729

Answer 2

A=1+1/3+1/3^2+......1/3^6

3A= 3 +1 + 1/3+......=1/3^5

3A-A= 3-1/3^6

A=\(\frac{3-\frac{1}{3^6}}{2}\)

Answer 3

\(A=1+\frac{1}{3}+\frac{1}{9}+\frac{1}{27}+\frac{1}{81}+\frac{1}{243}+\frac{1}{729}\)

\(A\)\(x\)\(3=3x\left(1+\frac{1}{3}+\frac{1}{9}+\frac{1}{27}+\frac{1}{81}+\frac{1}{243}+\frac{1}{729}\right)\)

\(A\)\(x3=3+1+\frac{1}{3}+\frac{1}{9}+\frac{1}{27}+\frac{1}{81}+\frac{1}{243}\)

\(A\)\(x3=1+\frac{1}{3}+\frac{1}{9}+\frac{1}{27}+\frac{1}{81}+\frac{1}{243}+3\)

\(-A=1+\frac{1}{3}+\frac{1}{9}+\frac{1}{27}+\frac{1}{81}+\frac{1}{243}+\frac{1}{729}\)

\(A\)\(x2=3-\frac{1}{729}=\frac{2186}{729}\)

\(A=\frac{2186}{729}:2=\frac{1093}{729}\)