A new bank was opening in Carolyn\'s town. As part of the marketing plan to encourage people to open savings accounts, they were giving away tickets for a drawing for a cash prize Carolyn opened a savings account and received a ticket. A month later the bank called to tell tier she had won The only problem was that she had to choose how she wanted to receive her cash prize: A) One thousand dollars all at once or B) Two dollars on the first day, four dollars on the second day, eight dollars on the third day sixteen on the fourth day, and so on for ten days in a row. How much would Carolyn receive if she chose the second option? Which prize should Carolyn choose in order to make the most money?
So, with second option she recieves $2 , $4 , $8 , ....till 10th day
So, its a gemetric series and we need to find sum of first ten terms
common ratio, r = 2 , nth term , an = a1(r)^n-1 =2(2)^n-1 = 2^n
Sum = a(1-r^n)/(1-r) = 2(1 -2^10)/(1-2)
= $ 2046 (with 2nd option)
She should select second option
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