Recurrence relation oddball one

[illidari]

Homework Statement

T(n) = 2^T(n-1)
T(1)=1

The Attempt at a Solution

I am trying to show the iterations.

T(n) = 2^T(n-1)
T(n) = 2^2T(n-2)
T(n) = 2^22T(n-3)

Is this the right track? Where the result would be 2^2222...1eventually?

The problem just feels awkward D:

If my answer is right is there any way to get this into a summation form?

 

[steve233]

Usually for these you start with a small n (or your base case) and start to look for a pattern.

T(1) = x
T(2) = x + something
T(3) = x + T(2)
.
.
.
T(n) = The summation of some pattern you found

Give that a try instead of looking for a pattern at step n.