Question
Find the constant c such that can be extended to be analytic at
, when
is fixed.
Answer :
Word Count : 124
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Consider ( f(z)=\dfrac{1}{z^{n}+z^{,n-1}+\cdots+z-n}+\dfrac{c}{z-1} ). Let ( g(z)=z^{n}+z^{,n-1}+\cdots+z=\sum_{k=1}^{n} z^{k} ), so the denominator of the first term is ( g(z)-n ). At ( z=1 ), ( g(1)=\sum_{k=1}^{n}1=n ),
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