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Let the power series be given with $$\sum_{n=0}^{\infty}3^nx^n$$ Find the sum function $f(x)$.

I know that $$\sum_{n=0}^{\infty}x^n=\frac{1}{1+x}$$ but I'm not sure how to find the sum function. I hope you will help.

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    $\begingroup$ Hint: $3^n\times x^n=(3x)^n$. $\endgroup$ – lulu Jun 19 at 11:14
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$$\sum_{n=0}^{\infty}3^nx^n=\sum_{n=0}^{\infty}(3x)^n=\frac{1}{1-3x}$$ provided that $|3x|<1$.

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    $\begingroup$ Consistency is important. $\endgroup$ – uniquesolution Jun 19 at 12:18

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