Superincreasing sequence

In mathematics, a sequence of positive real numbers $$(s_1, s_2, ...)$$ is called superincreasing if every element of the sequence is greater than the sum of all previous elements in the sequence.

Formally, this condition can be written as
 * $$s_{n+1} > \sum_{j=1}^n s_j$$

for all n ≥ 1.

Example
For example, (1, 3, 6, 13, 27, 52) is a superincreasing sequence, but (1, 3, 4, 9, 15, 25) is not. The following Python source code tests a sequence of numbers to determine if it is superincreasing:

This produces the following output:

Sum: 0 Element:  1 Sum: 1 Element:  3 Sum: 4 Element:  6 Sum: 10 Element:  13 Sum: 23 Element:  27 Sum: 50 Element:  52 Superincreasing sequence? True