marcelo1135 marcelo1135

07-03-2017
Mathematics

Answered

Use the power series representation of f(x)=\(\frac{1}{1-5x}\) to find a power series presentation of g(x)=\(\frac{15}{1-5x}\)

Verified Answer :

LammettHash LammettHash

05-05-2017

For \(|5x|<1\), 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 \(|5x|<1\).

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