Here's the question:

Find a power series representation for the function and determine the

interval of convergence.

f(x) = 1/(x + 10)

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- Feb 5th 2008, 11:08 AMUndefdisfigurePower series representation
Here's the question:

Find a power series representation for the function and determine the

interval of convergence.

f(x) = 1/(x + 10) - Feb 5th 2008, 11:15 AMJhevon
- Feb 5th 2008, 11:43 AMUndefdisfigure
Thanks Jhevon but before I even saw your answer I found the right method in the book and solved the power series representation and found that the interval of convergence is (-10, 10).

- Feb 5th 2008, 12:05 PMUndefdisfigure
Here's the question I REALLY should have asked. Its a little bit more challenging.

Find a power series representation for the function and determine the interval of convergence.

f(x) = x/(2x^2 + 1) - Feb 5th 2008, 12:17 PMJhevon
well, $\displaystyle \frac x{2x^2 + 1} = \frac d{dx} \frac 14 \ln (2x^2 + 1) = \frac 14 \frac d{dx} \ln (1 - (-2x^2))$

and you know the power series for $\displaystyle \ln (1 - x)$, so just find it's derivative and plug it in...

EDIT: in retrospect, it is perhaps easier to think of this as x times the power series of 1/(1 + 2x^2) ...oh well