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half-sums

Consider the infinite sum 96 + 48 + 24 + 12 + . . . , where each term is half the previous term and the pattern continues without end. The sum of the first ten terms is 191.8125. The addition of each new term gets you halfway between the sum of the previous terms and 192. So the sum gets very close to 192. Next, consider the sum 72 + (-36)+ 18 + (-9) + 4.5 + . . ., where each term is(-1/ 2) times the previous term and the pattern continues without end. This infinite sum also gets very close to some integer. Find this integer.

 Extensions
 Give an example of a list of numbers with an infinite sum equal to 80. (Source: Adapted from Mathematics Teaching in the Middle School, Mar-Apr 1997).

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