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Power Serieshard
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Let f(x)=x+2x2+3x3+⋯=∑n=1∞nxnf(x) = x + 2x^2 + 3x^3 + \cdots = \sum_{n=1}^{\infty} nx^nf(x)=x+2x2+3x3+⋯=∑n=1∞​nxn for ∣x∣<1|x| < 1∣x∣<1. If g(x)=f−1(x)g(x) = f^{-1}(x)g(x)=f−1(x) (the inverse function), what is the coefficient of x2x^2x2 in the power series g(x)=∑n=1∞bnxng(x) = \sum_{n=1}^{\infty} b_n x^ng(x)=∑n=1∞​bn​xn?