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ASHA 777 [7]
3 years ago
6

Use the power series representation of f(x)=

itle=" \frac{1}{1-5x} " alt=" \frac{1}{1-5x} " align="absmiddle" class="latex-formula"> to find a power series presentation of g(x)=\frac{15}{1-5x}
Mathematics
1 answer:
Sergeu [11.5K]3 years ago
4 0
For |5x|, we have

\dfrac1{1-5x}=\displaystyle\sum_{n\ge0}(5x)^n

and so

g(x)=\dfrac{15}{1-5x}=15\displaystyle\sum_{n\ge0}(5x)^n=3\sum_{n\ge0}5^{n+1}x^n

which is, again, only valid for |5x|.
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