Question 84882
A sequence of numbers each of which is progressively increased by the same factor, in this case, the factor is 2, is known as a geometric progression.
{{{2^0+2^1+2^2+2^3+2^4}}}+...+{{{2^(n-1)+2^n}}}
It can be shown that the sum of all the terms in such a progression is given by:
{{{S = 2^n - 1}}}
In your problem, n = 30 (the number of days), so, the total number of cents (S) received for 30-days work would be:
{{{S = 2^30 - 1}}} 
{{{S = 1073741824 - 1}}}
{{{S = 1073741823}}} cents. Multiply by 100 to find the number of dollars.
{{{S = 10737418.23}}}
The employee receives $10,737,418.23 for 30-days work.