(Solution Library) Find all values of x for which ∑_n=1^∞ (n x^n)/((n+1)(2 x+1)^n) converges
Question: Find all values of \(x\) for which
\[\sum_{n=1}^{\infty} \frac{n x^{n}}{(n+1)(2 x+1)^{n}}\]converges absolutely.
Deliverable: Word Document 
![[See] This exercise refers to the](/images/solutions/MC-solution-library-33560.jpg "[See] This exercise refers to the")
[See] This exercise refers to the "right side up" equilateral
(Steps Shown) Show that if ∑_n=1^∞ a_n converges, then
![[Solution Library] a. Show that ∑_n=1^∞ (n(n+1))/(x^n)=(2](/images/solutions/MC-solution-library-33562.jpg "[Solution Library] a. Show that ∑_n=1^∞ (n(n+1))/(x^n)=(2 x^2)/((x-1)^3)")
[Solution Library] a. Show that ∑_n=1^∞ (n(n+1))/(x^n)=(2 x^2)/((x-1)^3)
(See Solution) If p is a constant, show that the series 1+∑_n=3^∞
[Step-by-Step] The convergence of ∑_n=1^∞[(-1)^n-1 x^n]
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