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 badoumba March 7th, 2017 09:27 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 09:48 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 11:11 AM

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

 badoumba March 8th, 2017 02:26 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!

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