Example - Wrong Way

$T(n) = \left\{ \begin{array}{ll} \Theta(1) & {\rm if} \; n = 1 \\ T(n/3) + \Theta(n) & {\rm if} \; n > 1 \end{array} \right.$

T(n) = $\Theta(n)$ + T(n/3)
= $\Theta(n)$ + [ $\Theta(n/3)$ + T(n/3²)]
= $\Theta(n)$ + $\Theta(n)$ + T(n/3²)
Terminates when n/3ⁱ = 1, or i = log₃ n.
= $\sum_{i=0}^{log_3 n-1} \Theta(n)$ + T(1)
= $\Theta(n log_3 n)$ , not what we want!!!