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Find the coefficient of x n in the expansion of log(1+x+x 2 )

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

Grade:12

1 Answers

Badiuddin askIITians.ismu Expert
148 Points
13 years ago

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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