How can i make (x+x²+x³+x⁴+x⁵+x⁶+x⁷...) a function (meaning f(x)=...)?

Expert Answers

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The sum of the geometric series

`1+x+x^2+x^3+...`

is `(1)/(1-x)`

 

So your function would be:` `

`f(x)=x+x^2+x^3+...=(1)/(1-x)-1`

However, this function would only be valid if `-1<x<1`

If x is outside that range, you can't take the sum of 

 `x+x^2+x^3+...`

It doesn't "converge".  This sometimes happens when you sum up an infinite number of things.  For example, if you take `x=1`   then you are summing `1+1+1+1+1...` which is infinite.  So the only numbers where it is "legal" to add them all up, is: `-1<x<1`   

 

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