Please provide me a solution of Max-Heapify using Recursion Tree I tried my best to solve the recurrence relation.

$T(n) \le T(2n/3) + \Theta(1)$

Using the recursion tree.

I could reach out the boundary condition when at depth i:

$i= \log_{3/2}n$

Can someone please help me out in adding the costs and taking out the upper-bound.
I know at each depth the cost is increasing by a power of $2$, i:e- $2^i$.

What I have done so far is adding up the costs:

$\sum_{i=0}^{log_{3/2}n-1} 2^i+ \theta(log_{3/2}n)$.

Please correct me if I am wrong.
Thank you.
Try to solve the recurrent by expanding equality case:

$$T(n) = T(2n/3) + \Theta(1) = T(2^2n/3^3) + \Theta(1) + \Theta(1)$$

Now you can see $T(n) = \Theta(\log_{\frac{3}{2}}(n))$. Because each time $\Theta(1)$ is added up to reach to the leaf of the expnasion tree. 
Also, you can reach this result using the master theorem.