Find all values of x... (Infinite Sums)

Find all values of x for which the series converges, and find the sum of the series for those values of x. 

1/x^2 + 2/x^3 + 4/x^4 + 8/x^5 + 16/x^6 + ...

dont just show me the answer, I already know the answer. You must show me the steps you took to get to the answer. Also mind you I'm only a calculus student so don't do anything too advanced. 

The answer should be: Converges for |x| >2; S= 1/(x^2-2x)

  • I have a solution which doesn't use anything advanced, but 2$ is not worth the time to type it down. I'm happy to answer if you change the amount to something more reasonable.

  • In general, keep in mind that you're asking qualified professionals to spend their time giving you an answer. Just ask yourself how much money would you ask to solve and type out nicely the answer to a problem someone else gave you. I think it's safe to say that would be more than 2$.

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  • Leave a comment if you need any clarifications.

  • Just curious what is your qualifications exactly? Great job by the way.

  • I have a PhD in Math. Indeed most users who answer questions on the website have a PhD in math.

The answer is accepted.