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wcaprar
 3 years ago
Calc II problem. Sum of a series as a function of x?
wcaprar
 3 years ago
Calc II problem. Sum of a series as a function of x?

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wcaprar
 3 years ago
Best ResponseYou've already chosen the best response.0Find 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. \[\sum_{n=0}^{\infty} 9((x5)/9)^n\] series converges from 4 to 14. But how do I express the sum as a function of F(x)?

Thomas9
 3 years ago
Best ResponseYou've already chosen the best response.1As you might know, the following is true: \[\sum_{n=0}^\infty x^n=\frac{1}{1x}\] You can use that here: let's define y: \[y=\frac{x5}{9}\] we get: \[\sum_{n=0}^\infty 9y^n = \frac{9}{1y}\] and so: \[\sum_{n=0}^\infty 9 {\frac{x5}{9}}^n=\frac{9}{1\frac{x5}{9}}=\frac{81}{14x}\]
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