Well, i'm looking other Divergence and convergence tests for series other than divergence test, limit ratio test, ratio test. State the theorem as well. Thank you very much.
2006-08-14 00:57:10 · 3 answers · asked by Santos Lucipher 2 in Science & Mathematics ➔ Mathematics
Raabe's Test is a nice generalization of the ratio test:
Suppose that lim |a_{n+1} /a_n|=1 (the case where the ration test is inconclusive) and Let
L=lim n(|a_{n+1} /a_n| -1).
If L<-1, then the sum of a_n is absolutely convergent.
2006-08-14 02:59:55 · answer #1 · answered by mathematician 7 · 2⤊ 0⤋
This sequence will converge. look on the numerator: it rather is going to in basic terms oscillate, and could in no way exceed 2, no remember how super n turns into. so we are able to forget approximately with regard to the numerator for the needs of determining divergence/convergence. finding at in basic terms the denominator: a million/(n)(n)^(a million/3) = a million/n^(4/3) bear in mind the rule for a geometrical sequence: if the denominator is raised to the flexibility of something extra desirable than a million, it converges. If raised to the flexibility of a million or much less, it diverges. (4/3) > a million, so the sequence converges.
2016-10-02 01:36:00 · answer #2 · answered by ? 4 · 0⤊ 0⤋
And you haven't already checked the wikipedia? Shame.
http://en.wikipedia.org/wiki/Series_%28mathematics%29#Convergence_tests
2006-08-14 01:31:26 · answer #3 · answered by Pascal 7 · 0⤊ 1⤋