Maclaurin Series Expansion of 5ln(7-x)

[beanryu]

Represent the function 5ln(7-x) as a power series, i.e., Maclaurin series,

C_0=
C_1=
C_2=
C_3=
C_4=

i got C_0 = 5 ln (7-0)

and i think C_1 = 5/(7-1)

but its wrong

the textbook says that C_1 will be the derivative of C_0

anyway... please give me some hint

 

[Galileo]

You forgot to apply the chain rule.

 

[beanryu]

okay thanx

i got C_2 = -(5/7)

but how come C_3 is not -5/49

I think you just keep taking the derivative of the previous and set x = 0

am I wrong?

 

[Galileo]

I think you just keep taking the derivative of the previous and set x = 0

Ehm, no, that's not the expression for the n-th coefficient of a Taylor series. (which should be in your book).

But you can find out. If f function is written as:
$$f(x)=\sum_{n=0}^\infty c_n (x-a)^n$$
what is $c_n$ in terms of f and/or its derivatives? (Assume you can interchange differentiation and summation).