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Prove that the coefficient of x^n in the...

Prove that the coefficient of `x^n` in the expansion of `1/((1-x)(1-2x)(1-3x))i s1/2(3^(n+2)-2^(n+3)+1)dot`

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To prove that the coefficient of \( x^n \) in the expansion of \( \frac{1}{(1-x)(1-2x)(1-3x)} \) is \( \frac{1}{2}(3^{n+2} - 2^{n+3} + 1) \), we will use the method of partial fractions and series expansion. ### Step-by-Step Solution: 1. **Set Up the Partial Fraction Decomposition**: We start with the expression: \[ \frac{1}{(1-x)(1-2x)(1-3x)} ...
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