We define the first difference of a function by (x) = (x +
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We define the first difference δ ƒ of a function ƒ by δ ƒ(x) = ƒ(x + 1) − ƒ(x).
Suppose we can find a function P such that δP(x) = (x + 1)k and P(0) = 0. Prove that P(1) = 1k , P(2) = 1k + 2k, and, more generally, for every whole number n,
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P(n) = 1 + 2k + ... +n't
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