The constant term in the expansion of \( \left(1+\frac{1}{x}\right)^{20} \left(30x(1+x)^{29} + (1+x)^{30}\right) \) is
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To find the coefficient of \( x^k \) in \( x^m (1+x)^n \), you simply need to find the coefficient of \( x^{k-m} \) in the binomial expansion of \( (1+x)^n \), which is \( {}^{n}C_{k-m} \). Be careful with negative powers.