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1/3+1/2+c=1. Triangles: 1 3 6 10 15 21 28 where n is the last number in the sum. Shopping. The proof of the theorem is straightforward (and is omitted here); it can be done inductively via standard recurrences involving the Bernoulli numbers, or more elegantly via the generating function for the Bernoulli numbers. You don't have enough information to find the answer. &=2(1+2+3+\cdots+n)\\ To run this applet, you first enter the number n you wish to have illustrated; space limitations require 0