Question

Describe the pattern in the equation. Then solve the equation.

0.3x + 0.03x + 0.003x + 0.0003x + ....= 3

Answer 1

Each term is 10 times smaller than the previous one.


`0.3x+0.03x+0.003x+0.0003x+\ldots=3\\ x(0.3+0.03+0.003+0.0003+\ldots)=3\\ x\cdot0.\overline{3}=3\\ x\cdot(1)/(3)=3\\ x=9`