Question

Which represents the series 1+1/3+1/9+1/27 using sigma notation?

Answer 1

`\displaystyle 1+ (1)/(3) + (1)/(9) + (1)/(27) = (1)/(3^0)+ (1)/(3^1)+ (1)/(3^2) + (1)/(3^3) =\left( (1)/(3)\right)^0+\left( (1)/(3)\right)^1+\left( (1)/(3)\right)^2+\\\\\left( (1)/(3)\right)^3=\sum_(x=0)^3\left( (1)/(3)\right)^x \, \text{or }\, \sum_(i=1)^4\left( (1)/(3)\right)^(i-1)`