I understand simple factorials, but not factorial quotients where you have a numerator and denominator that don't simplify. I don't know what to do with expressions like 1 * 3 * 5 * 7 ..... (2n - 1).
There are two alternating series I'm stuck on. I am supposed to determine the convergence or divergence of the series using the Alternating Series Test: find where an is > 0; the limit of an as n approaches infinity must = 0; and you must show that a(n + 1) [the next nth term after an] is less than an for all values of n. We've been using derivatives to show a function is decreasing so I don't understand these mathematical induction style proofs.
1) Summation, from 1 to infinity:
[(-1)^(n + 1) * n!]/[1 * 3 * 5 . . . (2n - 1)]
2) Summation, from 1 to infinity :
[(-1)^(n + 1) * 1 * 3 * 5 . . . (2n - 1)]/[1 * 4 * 7 * . . . (3n - 2)]
If any math genius happens to see this, I would really be happy to have some help. Thanks. :)
2007-10-31
20:44:41
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3 answers
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asked by
Anonymous