(B) We have,$(1 + x + x^2 + ...)^{-n} = [(1 - x)^{-1}]^{-n} = (1 - x)^n$Using the binomial expansion for $(1 - x)^n$,we get:$(1 - x)^n = \sum_{k=0}^{n

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(B) We have,$(1 + x + x^2 + ...)^{-n} = [(1 - x)^{-1}]^{-n} = (1 - x)^n$Using the binomial expansion for $(1 - x)^n$,we get:$(1 - x)^n = \sum_{k=0}^{n} \binom{n}{k} (-x)^k = \binom{n}{0} - \binom{n}{1}x + \binom{n}{2}x^2 + ... + (-1)^n \binom{n}{n} x^n$The coefficient of $x^n$ is $(-1)^n \binom{n}{n} = (-1)^n \times 1 = (-1)^n$.