indefinite integral: (t/1-t^8) dt
need to show this as a power series, and the radius of convergence.
could use u sub i think.
thanks for any help.
$\displaystyle \frac{1}{1-x} = \sum_{n=0}^{\infty} x^n$, $\displaystyle |x|<1$.
Therefore, $\displaystyle \frac{1}{1-t^8} = \sum_{n=0}^{\infty} t^{8n}$, $\displaystyle |t| < 1$.
Thus, we get that $\displaystyle \frac{t}{1-t^8} = \sum_{n=0}^{\infty} t^{8n+1}$
Can you now integrate term-by-term?