How many segmentations are possible for a string length N? I have a string with length N. I would like to know how many segmentations are possible to it. 
Consider the example abcdc the number of N = 5
All possible segmentations are 

['abcdc']
['abcd', 'c']
['abc', 'dc']
['abc', 'd', 'c']
['ab', 'cdc']
['ab', 'cd', 'c']
['ab', 'c', 'dc']
['ab', 'c', 'd', 'c']
['a', 'bcdc']
['a', 'bcd', 'c']
['a', 'bc', 'dc']
['a', 'bc', 'd', 'c']
['a', 'b', 'cdc']
['a', 'b', 'cd', 'c']
['a', 'b', 'c', 'dc']
['a', 'b', 'c', 'd', 'c']


Then what will happen  when  my N tends to infinity . Any closed form equations?
There are n-1 points where you can break the string. Each is independent of the others. Therefore there are $2^{n-1}$ possibilities to break the string.