Let f(x)=∑n=0∞xnf(x) = \sum_{n=0}^{\infty} x^nf(x)=∑n=0∞xn and g(x)=∑n=1∞(−1)n+1nxng(x) = \sum_{n=1}^{\infty} \frac{(-1)^{n+1}}{n} x^ng(x)=∑n=1∞n(−1)n+1xn. Using the Cauchy product formula, find the coefficient of x3x^3x3 in f(x)⋅g(x)f(x) \cdot g(x)f(x)⋅g(x).
712\frac{7}{12}127
56\frac{5}{6}65
23\frac{2}{3}32
1112\frac{11}{12}1211