SOLVED:(a) Starting with the geometric series ∑n = 0^∞ x^n, find the sum of the series ∑n = 1^∞ nx^n - 1 |x |< 1 (b) Find the sum of each of the following series. (i) ∑n = 1^∞ nx^n, |x |< 1 (ii) ∑n = 1^∞ (n)/(2^n) (c) Find the sum of each of the following series. (i) ∑n = 2^∞ n(n - 1) x^n, |x |< 1 (ii) ∑n = 2^∞ (n^2 - n)/(2^n) (iii) ∑n = 1^∞ (n^2)/(2^n)
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