Question

"As first prize winner in a lottery, you are offered 1000000 in cash or a prize consisting of one cent on June

1, two cents on June 2, four cents on June 3, and so on,
with the amount doubling each day until the end of June
Which prize is more valuable? Explain.

Answer 1

Upon calculating the sum of the geometric series for the daily doubling penny amount, it is clear that this prize exceeds $1,000,000, making it more valuable than the $1,000,000 cash prize.

Step-by-step explanation:

To determine which prize is more valuable in the lottery scenario, we should calculate the total amount you would receive from the daily doubling penny amount versus the $1,000,000 cash prize. You receive one cent on June 1st, and the amount doubles each day until the end of June (30 days total).

The total amount for the doubling penny prize can be calculated using the formula for the sum of a geometric series, which is S = a(1-r^n)/(1-r), where a is the first term, r is the common ratio (doubling, so r=2), and n is the number of terms. Here, a is $0.01, r is 2, and n is 30. When you perform this calculation, you'll find that the sum exceeds $1,000,000.

Thus, the prize consisting of doubling pennies daily until the end of June is more valuable than the $1,000,000 cash prize.