Hello !!

Give the Taylor series about 0 for f and determine a range of validity for the series

Using the standard taylor series

Substituting

And taking 2 in the binomial series gives

Gives

as

Then

is valid for

Thanks Macca

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- Jul 22nd 2006, 05:24 AMmacca101Please check my work
Hello !!

Give the Taylor series about 0 for f and determine a range of validity for the series

Using the standard taylor series

Substituting

And taking 2 in the binomial series gives

Gives

as

Then

is valid for

Thanks Macca - Jul 22nd 2006, 06:41 AMQuickQuote:

Originally Posted by**macca101**

we have the taylor series:

and we have the series...

now let's solve for:

but let's say

then rewrite the problem:

and then let's say

now remembering the taylor series:

we see that must be between -1 and 1, let's figure out what needs to be between:

and solve from there...

~ - Jul 22nd 2006, 06:57 AMQuickQuote:

Originally Posted by**Quick**

I hope that's right.

Actually, I know I'm right :D - Jul 22nd 2006, 07:27 PMThePerfectHacker
How is that a Taylor series?

- Jul 22nd 2006, 07:40 PMQuickQuote:

Originally Posted by**ThePerfectHacker**

- Jul 23rd 2006, 02:18 AMmacca101Quote:

Originally Posted by**ThePerfectHacker**

What I was and sill am struggling with is finding the interval which the series is valid.

Quick gets it to

I have a math cad file that allows me to plot a Taylor series against the original function see below. This indicates to me the series is valid for approximately

http://ianmc.bulldoghome.com/pages/i...com/taylor.jpg

I hope I am making myself clear here I'm not saying quick is wrong (far be it from me) I just don't understand how to find the interval algebraically - Jul 23rd 2006, 09:02 AMThePerfectHackerQuote:

Originally Posted by**macca101**

---

I assume you want an infinite series for a function,

Note the infinite geometric,

for

Take derivative of both sides,

Substitute

Thus,

Good you got that right.

You are trying to find for what values this series converges.

You are going to use the generalized ratio test, with

Thus,

Its limit as, is 1/6,

Therefore the reciprocal of the limit tells you the radius of convergence which is 6.

Thus,

Same as saying,

- Jul 23rd 2006, 10:42 AMmacca101
Thanks For That