There is a long line of eager children outside of your house for trick-or-treating, and with good reason! Word has gotten around that you will give out 3k pieces of candy to the kth trick-or-treater to arrive. Children love you, dentists despise you. (a) Expressed in summation notation (using a Σ), what is cn, the total amount of candy that you should buy to accommodate n children total? (b) Use induction to prove that the total amount of candy that you need is given by the closed-form solution: cn = (3n+1 - 3) / 2
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