Find the coefficient of xⁿ in the expansion of log(1+x+x²)

Dear

log(1+x+x²)

log (1-x³)/(1-x)

log (1-x³) - log (1-x)

case when n is a multiple of 3

coefficient of xⁿ   is  -1/(n/3)      -(-1/n)

                                  = -2/n

when n is not a multiple of 3 then first term does not have a term xⁿ

 so coefficient of xⁿ  is -(-1/n)

                                        =1/n

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