A contest winner is given a choice of 2 prizes.

Prize 1:$1 today, $2 tomorrow, $4 on day 3 and so on, for 30 days. Each day the winner receives twice as much as the day before.

Prize 2: $1 today, $3 tomorrow, $9 on day 3, and so on, for 20 days. Each day the winner receives 3 times as much as the day before.
Which prize would you choose? Justify. Need the sum for each prize

compare the sums of the two geometric sequences:

(2^30 - 1)/(2-1)
vs
(3^20 - 1)/(3-1)

There's a difference, but either one will set you up for life!!

To determine which prize to choose, we need to calculate the sum for each prize over the respective number of days. Let's calculate the sums for both Prize 1 and Prize 2:

Prize 1:
The sum for each day in Prize 1 can be calculated using the formula: sum = (first term) * (1 - (common ratio)^(number of terms)) / (1 - (common ratio)). In this case, the first term is $1 and the common ratio is 2. We need to calculate the sum over 30 days, so the number of terms will be 30.

Using the formula, the sum for Prize 1 is:
sum = $1 * (1 - 2^30) / (1 - 2) = $1 * (-1073741823) / (-1) = $1,073,741,823

Prize 2:
Similarly, for Prize 2, the first term is $1 and the common ratio is 3. We need to calculate the sum over 20 days.

Using the formula, the sum for Prize 2 is:
sum = $1 * (1 - 3^20) / (1 - 3) = $1 * (-3486784399) / (-2) = $1,743,392,199.50

Now that we have the sums for both prizes, we can compare them. The sum for Prize 1 is $1,073,741,823, while the sum for Prize 2 is $1,743,392,199.50.

Therefore, based on the calculations, it is evident that Prize 2 has a higher sum compared to Prize 1. Therefore, if the goal is to maximize the total value received, the contestant should choose Prize 2.