Question

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

Answer 1

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

Answer 2

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

Answer 3

so whats in the sigma, thats important

Answer 4

thats what we have to try to find lol

Answer 5

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

Answer 6

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

Answer 7

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

Answer 8

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

Answer 9

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

Answer 10

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

Answer 11

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

Answer 12

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...

Answer 13

>.<

Answer 14

ha, I have no idea

Answer 15

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).

Answer 16

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

Answer 17

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.