find a power series representation for the function

• Apr 19th 2009, 12:29 AM
twilightstr
find a power series representation for the function
f(x) = ln(5-x) without using maclaurin series
• Apr 19th 2009, 12:47 AM
CaptainBlack
Quote:

Originally Posted by twilightstr
f(x) = ln(5-x) without using maclaurin series

for small $x\ge 0$:

$
f(x)=- \int_0^x \frac{1}{5-\xi} d\xi
$

Now use the binomial expansion for the integrand and integrate term by term.

CB
• Apr 19th 2009, 02:05 PM
twilightstr
i got ln5 - (1/5) sigma from n= 1 to infinity of (x/5)^n/(n) is this right?