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FP3 - Maclaurin Expansion watch

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    hey guys, having abit of a headach with this one:

    find the 1st 3 non zero terms for the expansion of
    ln (1 + X + X^2)

    if it's in the form of ln (1+A) what would A be? ive tried x(1+x) and (x+x^2)

    non of them seem to give the answer in the book.

    answer in book:

    X + (1/2)X^2 - (2/3)X^3..................

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    a = x + x^2, should do, post some workings out.
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    Okay, \ln(1+x)=\displaystyle\sum_{n=1}  ^{\infty} (-1)^{n+1}\frac{x^n}{n} So if you set A=x(1+x) you get:

    x(1+x) - \frac{(x(1+x))^2}{2}+\frac{(x(1+  x))^3}{3}-... expanding this should give you the desired answer. Post your working for that...
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    ln (1 + x +x^2)

    ln (1 + (x+x^2))

    (x+x^2) - [(x+x^2)^2]/2 + [(x+x^2)^3]/3

    *realized that i havent collected terms in x, x^2 and x^3

    x + x^2 - [x^2 + 2x^3 + x^4]/2 + [x^3 + 3x^4 + 3x^5 + 3x^6]/3

    x + (1/2)x^2 - (2/3)x^3....

    thanks guys!
 
 
 
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