What is the geometric power series?

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What is the geometric power series?

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Answer 1 · 2015-12-07T16:57:04

$a + a x + a x^{2} + a x^{3} + \dots$ $a+ax+ax^{2}+ax^{3}+cdots$ , which converges to $\frac{a}{1 - x}$ $a/(1-x)$ when $| x | < 1$ $|x|<1$ . More generally, you could also write $a + a (x - c) + a {(x - c)}^{2} + a {(x - c)}^{3} + \dots$ $a+a(x-c)+a(x-c)^{2}+a(x-c)^{3}+cdots$ , which converges to $\frac{a}{1 - (x - c)} = \frac{a}{(1 + c) - x}$ $a/(1-(x-c))=a/((1+c)-x)$ when $| x - c | < 1$ $|x-c| < 1$ .

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What is the geometric power series?

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