Omnimaga

General Discussion => Other Discussions => Math and Science => Topic started by: Yeong on December 11, 2012, 05:33:24 pm

Title: help with function → power series?
Post by: Yeong on December 11, 2012, 05:33:24 pm

Well I did fine on other questions until I reached this:

f(x) = ln (11-x)
                                      inf.
It's supposed to be ln 11 + sigma SOMETHING.
                                      n=1

How could I get this "SOMETHING" ?

Title: Re: help with function → power series?
Post by: Adriweb on December 11, 2012, 07:14:41 pm

Well, ln(11-x) = ln(11) + (- x/11 - x^2/242 - x^3/3993 - x^4/58564 - x^5/805255 ... )

and all that needs to be written in term of a sum...
not so sure how I can get there :/

looked at first like some kind of series development...

Maybe this can be of help :
(http://i.imgur.com/CY4AI.png)

More info here : http://www.wolframalpha.com/input/?i=ln%2811-x%29+-+ln%2811%29+


Edit : the denominator terms of the sum look like the one of  integral dx/(1+x)....
and its also linked to the binomial coeff of where you pick each time the 'n+1'th (or something) number of this serie http://oeis.org/A038325


Edit : from here : http://answers.yahoo.com/question/index?qid=20110124171309AAlDajr

  ∞
  Σ  -1/n (1/11)^n x^n + ln(11) = ln(11 - x)
n = 1