I'm trying to find the sum of $$\sum_{n=0}^∞ \frac{(3n)}{4^n}(-1)^n$$ So far I've tried finding the nth partial sum and finding the sum through the geometric series equation k/(1-r) to no avail.
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$$\sum_{n=0}^\infty nx^{n-1}=\dfrac1{(1-x)^2}$$ – J. W. Tanner Mar 26 '20 at 16:49
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@J.W.Tanner Thank you! You are a lifesaver. I didn't notice that but I'll always keep this in mind now. – rev Mar 26 '20 at 17:20