(a) Cans are stacked in a triangle on a shelf. The bottomrow contains k cans, the row
Chapter 9, Problem 57(choose chapter or problem)
(a) Cans are stacked in a triangle on a shelf. The bottomrow contains k cans, the row above contains one canfewer, and so on, until the top row, which has onecan. How many rows are there? Find an, the numberof cans in the nth row, 1 n k (where the toprow is n = 1).(b) Let Tn be the total number of cans in the top n rows.Find a recurrence relation for Tn in terms of Tn1.(c) Show that Tn = 12n(n + 1) satisfies the recurrencerelation.
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