# indefinite integral, power series

• February 4th 2009, 04:31 PM
rcmango
indefinite integral, power series
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.
• February 4th 2009, 04:50 PM
ThePerfectHacker
Quote:

Originally Posted by rcmango
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.

$\frac{1}{1-x} = \sum_{n=0}^{\infty} x^n$, $|x|<1$.
Therefore, $\frac{1}{1-t^8} = \sum_{n=0}^{\infty} t^{8n}$, $|t| < 1$.

Thus, we get that $\frac{t}{1-t^8} = \sum_{n=0}^{\infty} t^{8n+1}$

Can you now integrate term-by-term?