Power series. tell me if i'm on the right track.

[crazyformath2]

I have to find the power series f(x)= 3 / (2 -5x).

I devided everything by 2 so I have (1/2) / (1 - 5x/2) = $$\sum$$ ar^n

and then through some steps I have 15x^n / 2^n+1

and I on the right track? How do I find the interval of convergence?

 

[sutupidmath]

$$f(x)=\frac{3}{2-5x}=\frac{3}{2}*\frac{1}{1-\frac{5x}{2}}=\frac{3}{2}\sum_{n=0}^{\infty}[\frac{5}{2}x]^n$$

To find the radius of convergence u might want to use the ratio test.

 

[crazyformath2]

shouldnt that 5/2 x be negative though? does that make a difference?