Find a power series for the function.
$f(x) = \frac {6+x}{1-x} = (6+x)*\sum_{n=0}^{\infty}x^n=6\sum_{n=0}^{\infty}x^n + \sum_{n=0}^{\infty}x^{n+1}$
What do I have to do for the next step? Thank you.
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Collect like terms (i.e terms with the same exponent for $x$) – hmakholm left over Monica Apr 02 '16 at 22:25
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@HenningMakholm Oh, thanks for the idea! I find the power series. – devDNA Apr 02 '16 at 22:29
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Instead of editing "solved" into the question title, you should mark an answer as accepted (by clicking the green checkmark under the voting arrows). That will cause the question to be displayed in lists with a green background for its score that signifies "has an accepted answer". – hmakholm left over Monica Apr 02 '16 at 23:09
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@HenningMakholm oh, okay. thanks. :) – devDNA Apr 02 '16 at 23:50
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$$ f(x) = \frac {6+x}{1-x} = (6+x)*\sum_{n=0}^{\infty}x^n=6\sum_{n=0}^{\infty}x^n + \sum_{n=0}^{\infty}x^{n+1} $$ $$ 6\sum_{n=0}^{\infty}x^n + \sum_{n=1}^{\infty}x^{n} = 6\sum_{n=0}^{\infty}x^n + \sum_{n=0}^{\infty}x^{n} - 1 = \sum_{n=0}^{\infty}7x^n - 1 $$ you can stop there or say:
$$ f(x) = \sum_{n=0}^{\infty}(6 + \mbox{sgn}(n))x^n $$
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