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Let's solve each series numerically to test for convergence: ### Series (i): \[ \sum_{n=1}^{\infty} n X^{n-1}, \quad X > 0 \] This is a geometric series with a linear factor \(n\) in the numerator. To check for convergence, we can analyze the sum for different values of \(X\). ### ____ _______ _______ _________ __________.
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