Question: (a) Cans are stacked in a triangle on a shelf. The bottom row contains k cans, the row above contains one can fewer, and so on, until the top row, which has one can. How many rows are there? Find an, the number of cans in the nth row, 1 ≤ n ≤ k (where the top row 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 Tn-1.
(c) Show that Tn = ½n(n + 1) satisfies the recurrence relation.