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(4/8) - (5/9) + (6/10) - (7/11) + (8/12) - ....
is absolutely convergent, conditionally convergent or divergent
how do you tell the difference b/t these? can u plz explain them to me ...thnks!

2007-11-15 15:09:37 · 1 answers · asked by gistrm 1 in Science & Mathematics Mathematics

1 answers

A series can only be convergent if the individual terms converge to 0. If they don't, the series in divergent:

http://www.sosmath.com/calculus/series/convergence/convergence.html

In this case, the nth term has magnitude (4+n)/(8+n). What does this converge to as n gets larger?

For more details on the difference between different kinds of convergence (conditional convergence (aka semi-convergence) vs. absolute convergence) and the criteria for convergence, check out:
http://en.wikipedia.org/wiki/Series_(mathematics)

2007-11-18 02:46:45 · answer #1 · answered by simplicitus 7 · 0 0

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