The function is represented as a power series .

Find the first few coefficients in the power series.

Find the radius of convergence R of the series.

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- Jul 8th 2007, 11:33 AMvietpower series
The function is represented as a power series .

Find the first few coefficients in the power series.

Find the radius of convergence R of the series.

- Jul 8th 2007, 11:47 AMJhevon
To the first question: Recall that the power series expansion for is the series (this is derived by taking the derivative of the well know power series for )

So we have that:

therefore, we have

use that to find the first few coefficients

For the second question:

use the root test (or if you prefer, the ratio test, either one works nicely in this case) to find the radius of convergence. do you need help with that part? - Jul 9th 2007, 08:20 AMviet
yea looks like i need help on the second question

- Jul 9th 2007, 09:48 AMJhevon
Ok, we wish to find the radius of convergence for the series

Since you didn't specify what test you wanted me to use, I will pick one myself. I choose the root test, it's less typing than the ration**(why do i always do that?! type "ration" when i mean to type "ratio"!)**test in this case.

We have

we have convergence if

Thus the radius of convergence is