\nPut concisely, the limit ratio test looks at the following: limn->∞<\/sub>|tn+1<\/sub> ÷ tn<\/sub>|. If the limit < 1, then the series converges; if it's = 1, the test is inconclusive. If said limit > 1, then the series diverges.<\/p>\n \nThe limit ratio test is very useful, especially for factorials and other such awkward expressions. A quick example of the limit ratio test:<\/p>\n \nΣn!\/(n2n<\/sup>) (terms from n=0 to ∞) diverges because<\/p>\n \n|(n+1)!\/((n+1)2n+1<\/sup>) ÷ n!\/(n2n<\/sup>)| = |n!\/2n+1<\/sup> X 2n<\/sup>\/(n-1)!|<\/p>\n \nWhich simplifies to<\/p>\n \n|n\/2|, the limit of which, as n-> ∞, is > 1.<\/p>\n \nSource:<\/p>\n \nLarson, Roland E. and Robert P. Hostetler. Calculus, part one<\/em>, third edition. Toronto: D. C. Heath and Company, 1989.<\/p>\nJack of Oracle Tutoring by Jack and Diane,<\/a> Campbell River, BC. \n\n","protected":false},"excerpt":{"rendered":" Tutoring calculus, series convergence comes up. The tutor mentions the limit ratio test for convergence of an infinite series. Put concisely, the limit ratio test looks at the following: limn->∞|tn+1 ÷ tn|. If the limit < 1, then the series …\n\n