Chronology Current Month Current Thread Current Date
[Year List] [Month List (current year)] [Date Index] [Thread Index] [Thread Prev] [Thread Next] [Date Prev] [Date Next]

Re: Sum of Infinite Series



At 05:26 PM 1/24/02, you wrote:
...The top step (between blocks 1 and 2) is 1/2 block-length, the next step
down (between blocks 2 and 3) is 1/4 block-length, then 1/6, 1/8, 1/10,
1/12, and finally 1/14 block-length between blocks 7 and 8.

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


For computer types, the limit of the expression 1/2 + 1/4 + 1/8 + 1/16...
is readily given as one.
This leaves the series 1/6 + 1/10 + 1/12 + 1/14 + 1/18 + 1/20 ....

Taking the series 1/6 + 1/12 + 1/24... from it,
this is visibly 1/3 of the first series, and limits at 1/3

Taking the series 1/10 + 1/20 + 1/40 from it, this limits similarly at 1/5
Leaving us finally with a sum of 1 + 1/3 + 1/5 + 1/7 ....
which increases without limit as I recall, agreeing with my prejudice
that there is an offset stack which can grow without limit.
(I thought, with a constant width of overlap)
Brian Whatcott
Altus OK Eureka!