Concrete mathematics : a foundation for computer science

2.4 MULTIPLE SUMS 35
The middle term of this law is a sum over two indices. On the left, tj tk
stands for summing first on k, then on j. On the right, tk xi stands for
summing first on j, then on k. In practice when we want to evaluate a double
sum in closed form, it’s usually easier to sum it first on one index rather than
on the other; we get to choose whichever is more convenient.
Who’s panicking? Sums of sums are no reason to panic, but they can appear confusing to
I think this rule a beginner, so let’s do some more examples. The nine-term sum we began
is fairly obvious
compared to some
with provides a good illustration of the manipulation of double sums, because
of the stuff in that sum can actually be simplified, and the simplification process is typical
Chapter 1. of what we can do with x x’s:
x Cljbk = xCljbk[l