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Re: Sum of infinite series



On Sat, 26 Jan 2002, Paul O. Johnson wrote:

How would I easily find the sum of the first 50 or 100 terms
such as John Denker suggests in his second reply?

A spreadsheet is ideal for quick sums of finite series. Here are
a few results for 1/2 + 1/4 + 1/6 + 1/8 + ...

# of terms sum
10 1.4645
20 1.7989
50 2.2496
100 2.5937
200 2.9390
500 3.3964
1000 3.7427

As you can see, the series diverges painfully slowly.

I think it has been pointed out but it may be worth saying again
that this series is simply half of the well known "harmonic
series", 1 + 1/2 + 1/3 + 1/4 + ..., about which MUCH has been
written and can be found on the web. Here's a nice applet based
offering:

<http://www.shu.edu/projects/reals/numser/proofs/harmonic.html>

John Mallinckrodt mailto:ajm@csupomona.edu
Cal Poly Pomona http://www.csupomona.edu/~ajm