My Math Forum Sum equation problem

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 March 7th, 2017, 09:27 AM #1 Newbie   Joined: Mar 2017 From: Paris Posts: 3 Thanks: 0 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
March 7th, 2017, 09:48 AM   #2
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Quote:
 Originally Posted by badoumba 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.

 March 7th, 2017, 11:11 AM #3 Newbie   Joined: Mar 2017 From: Paris Posts: 3 Thanks: 0 Thanks Romsek ! I can now extract n with a logx. Easy.
 March 8th, 2017, 02:26 PM #4 Newbie   Joined: Mar 2017 From: Paris Posts: 3 Thanks: 0 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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