Re: Sum of Infinite Series

["John S. Denker" <jsd@MONMOUTH.COM>]

> "Paul O. Johnson" wrote:
>
> .... requires that I sum the infinite series 1/2 + 1/4 +
> 1/6 + 1/8 + . . .

Grind out the Taylor series for -log(1+x).
You're interested in the limit as x -> -1.
That's right at the edge of the radius of
convergence, obviously, so you don't want
to set x exactly equal to -1.

John Mallinckrodt wrote:
> The series diverges.  Thus, an arbitrary extension is
> theoretically possible.

Right.  But that doesn't answer the question.

> In practice, you'll be *very* lucky to get an extension
> of two block lengths!

It'll take more than luck to do _that_ with the available
number of blocks (eight).

But it's no great trick to build something where the top
block has nowhere near any overlap with the supporting
table.