Question

A sweepstakes give away $1 000 000 prizes the first ticket drawn wins $5 , the second ticket drawn wins $15 , the third drawn wins $45 , and so on .
1) how many tickets can sweepstakes afford to draw ?
2) how much money is left after all the prizes are awarded ?

Answer 1

The sum of 5 * 3^k (from k=0 to n) <= 1 million.
The sum of 3^k (from k=0 to n) <= 200,000
Floor[3^(n+1) / 2] <= 200,000
3^(anything) is odd, so Floor[3^(n+1) / 2] = [3^(n+1) - 1] / 2
3^(n+1) <= 400,001

Now solve for n.