Finding the coefficient of \(\displaystyle{x}^{{n}}\) in the

Alan Zavala

Alan Zavala

Answered question

2022-04-07

Finding the coefficient of xn in the expansion of {({loge(1+x)})2}
I've been trying to find the coefficient of xn in the expansion of ({loge(1+x)})2.I wrote out the expansion of {({loge(1+x)})2} explicitly and tried to generalize the terms involving xn, but...so far no luck.
Is there any other alternative ?

Answer & Explanation

Wernbergbo9d

Wernbergbo9d

Beginner2022-04-08Added 12 answers

Squaring log(1+x)=xx22+x33 one obtains the following coefficient of xn:
k=1n1(1)n1k(nk)=(1)nnk=1n11k+1nk=(1)n2Hn1n.

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