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.

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- Feb 4th 2009, 04:31 PMrcmangoindefinite 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. - Feb 4th 2009, 04:50 PMThePerfectHacker
$\displaystyle \frac{1}{1-x} = \sum_{n=0}^{\infty} x^n$, $\displaystyle |x|<1$.

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?