As you have probably discovered by now, as we use larger and larger limits in
the summation, we keep getting larger and larger answers. Will this continue
indefinitely, or is there some limit beyond which the sum cannot go?
Mathematically speaking, what we are wondering is whether
is finite or infinite. That is, as n approaches infinity, does the sum also
approach infinity or does it get ``stuck'' at some finite value. Perhaps not
surprisingly, Maple provides a built-in function to compute limits. Here is
how we can turn the bit of mathematics above into a Maple computation:
| limit(sum(1/(2*'i'), i=1..'n'), 'n'=infinity); |
Maple tells us that the limit is infinity. This means that in principle, given
enough blocks and enough patience, we can build a stack of bricks that extends
arbitrarily far out beyond the edge of the table! Is that what you expected
when you began this problem?
Joseph L. Zachary
Hamlet Project
Department of Computer Science
University of Utah