Find a power series representation for the function, and find the interval of convergence: 1/(1-x^3)

Question

anonymous · Answer

looks just like 
$$\frac{1}{1-x}=\sum x^n$$ only with $x^3$ instead of $x$

anonymous · Answer

replace $x$ by $x^3$ and you are done

anonymous · Answer

btw same radius of convergence, since $|x|<1\iff |x^3|<1$

anonymous · Answer

Wait so the answer is the same thing? There are no major steps? Can you lead me through it...?

anonymous · Answer

@satellite73

kirbykirby · Answer

There really isn't much other than to replace $x$ by $x^3$ as satellite said. In their first reply, they gave you the series representation for 1/(1-x). If you just change the $x$ to $x^3$, then you just replace $x$ with $x^3$ on the right hand side: $\large \sum (x^3)^n$.

The idea is to see if your given series can "look" like the basic series you know for $1/(1-x)$.

kirbykirby · Answer

It may seem a bit trivial, but maybe it will make more sense as you do more of these types of problems.