marcelo1135
contestada

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

Respuesta :

LammettHash
For [tex]|5x|<1[/tex], we have

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

and so

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

which is, again, only valid for [tex]|5x|<1[/tex].

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