How Do You Solve x+x^2+x^3+x^4... = 14 for x?

[Niaboc67]

x+x^2+x^3+x^4... = 14

Find x

Could someone please provide an explanation on how to solve this?

 

[ShayanJ]

The formula for infinite geometric series is $\displaystyle \sum_{n=0}^\infty a_n x^n =\frac{a_0}{1-x}$. But this is true only for $-1 < x < 1$. Just use this on the series to get an equation in a familiar form.

 

[Mark44]

Same question asked in another thread with the same name, so locking this thread.

@Niaboc67, please don't start multiple threads on the same topic.