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


is `(1)/(1-x)`


So your function would be:` `


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

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


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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