Algebra Pre-Algebra and Basic Algebra Math Forum

 October 8th, 2016, 06:21 PM #1 Newbie   Joined: Jan 2012 Posts: 2 Thanks: 0 Reverse an equation containing a sum Hello, I currently have the following equation: $\displaystyle y = (\sum_{n=1}^{z} (n + 300 * 2^{{z}/{7}})) / 4$ If we give us z, I have no trouble finding y, but if we get y how can we get z? Having trouble reversing the equation... Trying to isolate z, but no idea on how to proceed with the sum. $\displaystyle 4 * y = \sum_{n=1}^{z} (n + 300 * 2^{z/7})$ October 8th, 2016, 07:39 PM #2 Math Team   Joined: Dec 2013 From: Colombia Posts: 7,700 Thanks: 2682 Math Focus: Mainly analysis and algebra I don't think the final term is correct. $$\sum_{n=1}^{7m} 2^m = 2\sum_{n=0}^{7m-1} 2^m$$ \begin{align*} \text{if} \quad S &= 2(1+2+4+8+\ldots+2^{7m-1}) \\ 2S &= 2(\phantom{1+}2+4+8+\ldots+2^{7m-1}+2^{7m}) \\ S &= 2(2^{7m} -1) \\ \end{align*} Thus, with $z=7m$ we have the final terms as $75 \times 2(2^z-1)$. October 8th, 2016, 07:46 PM #3 Senior Member   Joined: Sep 2015 From: USA Posts: 2,647 Thanks: 1476 thought I had deleted it October 8th, 2016, 09:44 PM #4 Math Team   Joined: Dec 2013 From: Colombia Posts: 7,700 Thanks: 2682 Math Focus: Mainly analysis and algebra I must have got there before you did. Looking at it, what I wrote isn't correct either. Your one probably was (although I can't remember it exactly). October 8th, 2016, 09:48 PM   #5
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Joined: Sep 2015
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Quote:
 Originally Posted by v8archie I must have got there before you did. Looking at it, what I wrote isn't correct either. Your one probably was (although I can't remember it exactly).
It agreed with Mathematica, but when I saw that there was no closed form solution I meant to leave it for someone else to take a look at and thought I deleted it.

Last edited by skipjack; October 9th, 2016 at 07:02 AM. Tags equation, reverse, 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 vdrn Number Theory 28 October 22nd, 2011 05:07 PM swtrse Number Theory 2 August 6th, 2009 05:53 AM NumberA Algebra 5 April 19th, 2009 12:03 PM artheus Trigonometry 5 February 22nd, 2009 06:21 PM Clox Algebra 2 January 23rd, 2008 01:24 AM

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