Question

Use the power series representation of f(x)=
`(1)/(1-5x)` to find a power series presentation of g(x)=
`(15)/(1-5x)`

Answer 1

For
`|5x|<1`, we have


`\frac1{1-5x}=\displaystyle\sum_(n\ge0)(5x)^n`

and so


`g(x)=(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`.