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).
Calculate δ(x3), δ(x2), and δ(x). Then find a polynomial P of degree 3 such that δP = (x + 1)2 and P(0) = 0. Conclude that P(n) = 12 + 22 + · · · + n2.
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Lets start by calculating the first differences of the given functions 1 x3 x3 x 13 x3 Expanding ...View the full answer
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