# How do I prove that ∑(n=1) to ∞ nx^n, |x|<1, is equal to x/(1-x)^2?The proof should manipulate the finite partial sums and then take a limit?

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• How do I prove that ∑(n=1) to ∞ nx^n, |x|<1, is equal to x/(1-x)^2?The proof should manipulate the finite partial sums and then take a limit?

Power rule. If f: R → R {\displaystyle f:\mathbb {R} \rightarrow \mathbb {R} } is a function such that f (x) = x r {\displaystyle f(x)=x^{r ...
Positive: 91 %
... as x!1, X n p x naB r nx n o = O ... n=1 (n)xn; (1.16) respectively, then1 X1 n=1 ˚(n)e n = ... Proof. Take = 0, = 1, ...
Positive: 88 %

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I have tried evaluating this series $$\sum_{n=1}^{\infty}\frac{H_{n}^3}{(n+1)2^n}$$ using some methods but it's seems to me that it is very hard.
Positive: 91 %
... i.e. x, for any x : 1 → X. Inthis ... ˜ f 0 i##GGGGGGGGG Ns//x??Nx??N × B At//N × B Awhere ... Then F is an equivalence ofC and Set.Proof. Given g
Positive: 86 %
... (x) = cos(nx), n = 1;2;3;4;::: ... Prove as seguintes aﬂrma ... Encontre a melhor aproxima»c~ao por m¶‡nimos quadr¶aticos da solu»c~ao do ...