My Math Forum

My Math Forum (http://mymathforum.com/math-forums.php)
-   Probability and Statistics (http://mymathforum.com/probability-statistics/)
-   -   Sum equation problem (http://mymathforum.com/probability-statistics/339419-sum-equation-problem.html)

badoumba March 7th, 2017 08:27 AM

Sum equation problem
 
Hi everyone.

I have an equation to solve - don't know how to proceed.

$\displaystyle \sum_{i=0}^n(1.1*x)^n=y$

x and y are known values.
I need to figure out the value of n.

Any tips out there? :)
Thanks

romsek March 7th, 2017 08:48 AM

Quote:

Originally Posted by badoumba (Post 563749)
Hi everyone.

I have an equation to solve - don't know how to proceed.

$\displaystyle \sum_{i=0}^n(1.1*x)^n=y$

x and y are known values.
I need to figure out the value of n.

Any tips out there? :)
Thanks

$\displaystyle{\sum_{i=0}^n}~(a x)^n = \dfrac{1-(a x)^{n+1}}{1-a x}$

solving this should be pretty straightforward now.

badoumba March 7th, 2017 10:11 AM

Thanks Romsek !
I can now extract n with a logx. Easy.

badoumba March 8th, 2017 01:26 PM

Conversely, what about if I am interesting in figure out what is the value of x, knowing all the other variables?

This is equivalent to the following: let's say I have :
$\displaystyle x^0+x^1+x²+x³=17$

How can I calculate x? If I use the same above formula, I have an equation with x^(n+1)+ax+c.

Thanks!


All times are GMT -8. The time now is 04:22 AM.

Copyright © 2018 My Math Forum. All rights reserved.