- #1

- 90

- 3

Using:

[tex] \frac{1}{1-x} = \sum_{i=0}^{\infty} x^{i} , |x|<0 [/tex]

Find the power series representation and interval of convergence for:

[tex]f(x) = \frac{1}{(1-3x)^{2}} [/tex]

We have that:

[tex] \frac{d}{dx}\left[\frac{1}{1-x}\right] = \frac{1}{(1-x)^{2}} = \sum_{i=0}^{\infty} ix^{i-1} , |x| < 0 [/tex]

Of all things, the algebra of manipulating the function in question is stumping me. For some reason whatever I try doesn't seem to work.