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**Extra info for Concrete Mathematics: A Foundation for Computer Science (1st Edition)**

**Example text**

Such considerations motivate the following manipulations. We have Sq = x CljClk l

1 l/6 = 55. Incidentally, page 72 of the CRC Tables has further information about the sums of cubes, . . , tenth powers. The definitive reference for mathematical formulas is the Handbook of Mathematical Functions, edited by Abramowitz and Stegun [2]. 38), together with the analogous formulas for sums of cubes, . . , fifteenth powers, with or without alternating signs. But the best source for answers to questions about sequences is an amazing little book called the Handbook of Integer Sequences, by Sloane [270], which lists thousands of sequences by their numerical values.

L. 6 FINITE AND INFINITE CALCULUS 49 example, C might be the periodic function a + b sin2nx; such functions get washed out when we take differences, just as constants get washed out when we take derivatives. At integer values of x, the function C is constant. Now we’re almost ready for the punch line. Infinite calculus also has definite integrals: If g(x) = Df(x), then /‘g(x)dx = f(x)11 = f(b) -f(a). a Therefore finite calculus-ever mimicking its more famous cousin- has definite Sims: If g(x) = Af(x), then Lb g(x) 6x = f(x)i’ = f(b) -f(a).