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 October 26th, 2017, 02:36 AM #1 Member   Joined: Aug 2013 Posts: 41 Thanks: 3 Limiting sum Suppose a Geometric series has a limiting sum = 2. Find the values of the first term 'a'. Its rather easy to show that 0
 October 26th, 2017, 03:24 AM #2 Math Team   Joined: Jan 2015 From: Alabama Posts: 3,264 Thanks: 902 A geometric series is of the form $\displaystyle \sum_{n=0}^\infty ar^n$ for given number a and r and its "limiting sum" (I would say just "sum") is given by $\displaystyle \frac{a}{1- r}$. If that "limiting sum" is 2 then we have $\displaystyle \frac{a}{1- r}= 2$ so $\displaystyle a= 2(1- r)$. In order that the "limiting sum" exist, we must have $\displaystyle -1< r< 1$ so that $\displaystyle -1< -r< 1$, $\displaystyle 0< 1- r< 2$, and $\displaystyle 0< 2(1- r)< 4$. a, the first term in the series, can be any number between 0 and 4. Yes, r can be 0 so a can be 1. In that case, as you say, the "geometric sum" is just 2+ 0+ 0+ .... Thanks from evaeva Tags limiting, 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 bezan Calculus 3 November 5th, 2013 11:25 PM One Calculus 11 April 9th, 2013 03:36 PM problem Advanced Statistics 1 November 2nd, 2009 01:36 PM illusion Advanced Statistics 0 December 4th, 2007 11:32 AM illusion Advanced Statistics 0 December 4th, 2007 11:28 AM

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