2012 UNCO Math Contest II Problems/Problem 9
Treasure Chest . You have a long row of boxes. The 1st box contains no coin. The next boxes each contain coin. The next boxes each contain coins. The next boxes each contain coins. And so on, so that there are boxes containing exactly coins.
(a) If you combine the coins from all the boxes that contain , or coins you get coins. How many coins do you get when you combine the coins from all the boxes that contain or coins? Give a closed formula in terms of . That is, give a formula that does not use ellipsis or summation notation.
(b) Combine the coins from the first boxes. What is the smallest value of for which the total number of coins exceeds ? (Remember to count the first box.)
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