Sum of infinite series

[Laurent Hodges <lhodges@IASTATE.EDU>]

> I want to state in the exhibit's sign what the absolute maximum extension
> is. This requires that I sum the infinite series 1/2 + 1/4 + 1/6 + 1/8 + . . .
> Paul O. Johnson

This can be grouped, after the first two terms, into 2 terms each larger
than or equal to 1/8 (thus summing to over 1/4), followed by 4 terms each
larger than or equal to 1/16 (thus summing to over 1/4), followed by 8
terms each larger than or equal to 1/32 (thus summing to over 1/4), etc.
The sum is thus at least 1/4 + 1/4 + 1/4 + ..., which is clearly is
infinite, so the series diverges.  This is probably the easiest way to see
this, without appealing to integrals and the like.


Laurent Hodges, Professor of Physics
12 Physics Hall, Iowa State University, Ames, IA  50011-3160
lhodges@iastate.edu   http://www.public.iastate.edu/~lhodges