My Math Forum  

Go Back   My Math Forum > High School Math Forum > Algebra

Algebra Pre-Algebra and Basic Algebra Math Forum


Reply
 
LinkBack Thread Tools Display Modes
October 8th, 2016, 05:21 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.
$\displaystyle 4 * y = \sum_{n=1}^{z} (n + 300 * 2^{z/7})$
chocapic is offline  
 
October 8th, 2016, 06:39 PM   #2
Math Team
 
Joined: Dec 2013
From: Colombia

Posts: 7,671
Thanks: 2651

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 $75 \times 2(2^z-1)$.
v8archie is offline  
October 8th, 2016, 06:46 PM   #3
Senior Member
 
romsek's Avatar
 
Joined: Sep 2015
From: USA

Posts: 2,500
Thanks: 1372

thought I had deleted it
romsek is offline  
October 8th, 2016, 08:44 PM   #4
Math Team
 
Joined: Dec 2013
From: Colombia

Posts: 7,671
Thanks: 2651

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).
v8archie is offline  
October 8th, 2016, 08:48 PM   #5
Senior Member
 
romsek's Avatar
 
Joined: Sep 2015
From: USA

Posts: 2,500
Thanks: 1372

Quote:
Originally Posted by v8archie View Post
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 06:02 AM.
romsek is offline  
Reply

  My Math Forum > High School Math Forum > Algebra

Tags
equation, reverse, sum



Thread Tools
Display Modes


Similar Threads
Thread Thread Starter Forum Replies Last Post
reverse n vdrn Number Theory 28 October 22nd, 2011 04:07 PM
Reverse Modulo swtrse Number Theory 2 August 6th, 2009 04:53 AM
Reverse solve f(x)? NumberA Algebra 5 April 19th, 2009 11:03 AM
How to reverse arc tangent and sinus equation? artheus Trigonometry 5 February 22nd, 2009 05:21 PM
Reverse calculation Clox Algebra 2 January 23rd, 2008 12:24 AM





Copyright © 2019 My Math Forum. All rights reserved.