Example - Right Way

T(n) = $\Theta(n)$ + T(n/3)
= $\Theta(n)$ + [ $\Theta(n/3)$ + T(n/3²)]
= $\Theta(n)$ + $\Theta(n/3)$ + T(n/3²)
= $\Theta(n)$ + $\Theta(n/3)$ + $\Theta(n/3^2)$ + T(n/3³)
= $\sum_{i=0}^{log_3 n-1} \; \Theta(n/3^i)$ + T(1)
= $\Theta(n \sum_{i=0}^{log_3 n-1} \; (1/3)^i)$ + T(1)
= $\Theta(n (\frac{(1/3)^{log_3 n} - 1}{1/3 - 1}))$ + T(1)
= $\Theta(3/2n(1 - 1/n))$ + T(1)
= $\Theta(\frac{3n}{2} - \frac{3n}{n})$ + T(1)
= $\Theta(n)$