Suppose you're given a job that lasts for one month (31 days). You get one cent on the first day, two cents on the second, 4 on the third, etc.

What's the total amount you would make?

I know the formula to calculate the amount has something to do with 2^(n-1) for the amount received on the last day... and I know that (2^n)-1 has something to do with summarizing the total amount, but I'm not sure where to go.

I'm not looking for an outright answer, but just something to understand why those formulas are necessary and how to head off in the right direction. Thanks!