Concrete mathematics : a foundation for computer science

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2.6 FINITE AND INFINITE CALCULUS 51
In particular, when m = 1 we have kl = k, so the principles of finite
calculus give us an easy way to remember the fact that
ix
OS-kin
k = f = n(n-1)/2
The definite-sum method also gives us an inkling that sums over the range
0 $ k < n often turn out to be simpler than sums over 1 < k 6 n; the former
are just f(n) - f (0)) while the latter must be evaluated as f (n + 1) - f ( 1)
Ordinary powers can also be summed in this new way, if we first express
them in terms of falling powers. For example,
hence
t
OSk