## anonymous 5 years ago What is a Taylor Series for f(x)=ln(2+2x) ?

1. anonymous

ummm I might be able to do this... we'll need to collaborate though

2. anonymous

they gave the first part: ln(2)+$\sum_{n=1}^{\infty}$

3. anonymous

so whats in the sigma, thats important

4. anonymous

thats what we have to try to find lol

5. anonymous

does the question say exactly that? What is a taylor series for...

6. anonymous

take the derivative of ln(x) like 4 or 5 times see if you can see a pattern

7. anonymous

yes, What is a Taylor Series for f(x)=ln(2+2x)

8. anonymous

of and at x=1/2 we know that ln(1) = 0

9. anonymous

$\sum_{?}^{?} (f^{(n)}(1/2))/n! * (2x-(1/2))^{n}$

10. anonymous

the general formula would be F^(n) (x) = (-1)^(n+1) (n-1) ! --------------- x^(n)

11. anonymous

thats my best guess but I think I'm taking it too fat by kinda approxximating

12. anonymous

yes it would now try writing that in sigma notation which is what I did up there...not sure if this is right to do...

13. anonymous

>.<

14. anonymous

ha, I have no idea

15. anonymous

Go to the general form of the Taylor Series. T(x) = f(a) + f'(a)(x-a) + f''(a)(x-a)^2/2! + ... and plug the derivatives of ln(2+2x) into the places you see fit (I think in this case it's safe to set a=0).

16. anonymous

I dont know where I would stop using the general form...?

17. anonymous

Until you see the general form that they're taking...and then you can put the general form of the series into your sum symbol.