Calc II problem. Sum of a series as a function of x?

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Calc II problem. Sum of a series as a function of x?

Mathematics
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At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.

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Find all values of x for which the series converges. For these values of x, write the sum of the series as a function of x. \[\sum_{n=0}^{\infty} 9((x-5)/9)^n\] series converges from -4 to 14. But how do I express the sum as a function of F(x)?
As you might know, the following is true: \[\sum_{n=0}^\infty x^n=\frac{1}{1-x}\] You can use that here: let's define y: \[y=\frac{x-5}{9}\] we get: \[\sum_{n=0}^\infty 9y^n = \frac{9}{1-y}\] and so: \[\sum_{n=0}^\infty 9 {\frac{x-5}{9}}^n=\frac{9}{1-\frac{x-5}{9}}=\frac{81}{14-x}\]

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