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 March 19th, 2019, 07:37 AM #1 Senior Member   Joined: Jul 2011 Posts: 407 Thanks: 16 Series sum The sum of series $$\frac{5}{2!\cdot 3}+\frac{5\cdot 7}{3!\cdot 3^3}+\frac{5\cdot 7\cdot 9}{4!\cdot 3^3}+\cdots \cdots \infty$$ March 19th, 2019, 11:04 AM #2 Senior Member   Joined: Sep 2015 From: USA Posts: 2,633 Thanks: 1472 should the denominator of the 2nd term be $3! \cdot 3^2$ ? Otherwise I don't see the pattern. March 19th, 2019, 11:43 AM   #3
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 Originally Posted by panky The sum of series $$\frac{5}{2!\cdot 3}+\frac{5\cdot 7}{3!\cdot 3^2}+\frac{5\cdot 7\cdot 9}{4!\cdot 3^3}+\cdots \cdots \infty$$ March 27th, 2019, 02:55 PM #4 Senior Member   Joined: Dec 2015 From: Earth Posts: 820 Thanks: 113 Math Focus: Elementary Math The sum can be written as $\displaystyle \sum_{n=2}^{\infty} \frac{\prod_{n=2}^{\infty} (1+2n) }{3^{n-1} n! }$ . To compute it seems complicated. March 27th, 2019, 03:51 PM #5 Global Moderator   Joined: Dec 2006 Posts: 21,105 Thanks: 2324 The sum should be written as $\displaystyle \sum_{n=2}^\infty \frac\prod_{k=2}^n (2k + 1)}{3^{n-1}n!$, which evaluates to 3√3 - 2 according to W|A. Thanks from topsquark and idontknow Tags series, sum 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 akerkarprash Computer Science 1 March 10th, 2019 11:56 AM stevewilliams Algebra 1 April 22nd, 2016 02:40 PM king.oslo Complex Analysis 0 December 28th, 2014 07:50 AM The Chaz Real Analysis 11 February 7th, 2011 05:52 AM g0bearmon Calculus 1 December 31st, 1969 04:00 PM

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