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 Algebra Pre-Algebra and Basic Algebra Math Forum

 February 15th, 2019, 01:32 PM #1 Banned Camp   Joined: Feb 2019 From: Casablanca Posts: 23 Thanks: 2 weird series Hello everyone Here is a $Z_n$ Suite $\displaystyle Z_3 = 1/2$ $\displaystyle Z_n = Z_ {n + 1} / \cos ({\pi} / {n})$ It's a bizarre suite decreasing to 0 without ever going. I will define the n with which I work in my suite so as not to fall into absurdities like 1/0 which gives false calculations. find that $\displaystyle n = \pi / \arccos (Z_{n + 1} / Z_n)$ Note that $Z_n \ne 0$ and $(Z_{n + 1} / Z_n) \ne 1$, so the $Z_n$ limit is non-zero. And since I have a decreasing sequence, $\displaystyle Z_{n + 1} / Z_n < 1$, so the series $Z_n$ is convergent according to the d'Alembert criterion. Is there an error in this reasoning? $Z_n$ is a positive term and is decreasing and minus 0 tends to 0 minus bound 0, which is impossible because $Z_n \ne 0$, no? Last edited by skipjack; February 15th, 2019 at 01:48 PM. Tags series, weird Thread Tools Show Printable Version Email this Page Display Modes Linear Mode Switch to Hybrid Mode Switch to Threaded Mode Similar Threads Thread Thread Starter Forum Replies Last Post Jopus Number Theory 1 April 30th, 2015 12:13 PM evaldivieso Calculus 9 February 13th, 2013 08:50 AM evaldivieso Calculus 2 February 13th, 2013 07:41 AM brsystem Calculus 2 October 6th, 2012 02:29 PM shin777 Algebra 4 November 29th, 2011 11:45 AM

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