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 Dec 16 awarded Popular Question Dec 9 comment Proving that $\sum_j x^j$ is differentiable $(-1,1)$ Ah, so it converges on every interval $[-\beta, \beta]$ for $|\beta| < 1$? Many thanks for your help @EricAuld Dec 8 revised Proving that $\sum_j x^j$ is differentiable $(-1,1)$ added 436 characters in body Dec 8 comment Proving that $\sum_j x^j$ is differentiable $(-1,1)$ Yes but I am not sure how to show that $\sum_j (j+1)x^j$ converges to a finite number for $|x| < 1$? Dec 8 revised Showing that $\sum_j e^{-jx}x^j$ converges uniformly added 17 characters in body Dec 8 asked Proving that $\sum_j x^j$ is differentiable $(-1,1)$ Dec 8 accepted Showing that $\sum_j e^{-jx}x^j$ converges uniformly Dec 8 comment Showing that $\sum_j e^{-jx}x^j$ converges uniformly Hmm, thanks Mhenni! Any idea as to how I would actually compute the sum? Dec 8 asked Showing that $\sum_j e^{-jx}x^j$ converges uniformly Dec 3 accepted How to prove Riemann integrable with partitions Nov 18 accepted How to show that $\sum {2^j + j \over 3^j - j}$ converges Nov 16 asked How to show that $\sum {2^j + j \over 3^j - j}$ converges Nov 8 comment How to prove Riemann integrable with partitions I understand, however, I am trying to prove this Riemann integrability from first principles, and so would like to find a way that involves a choice of partition rather than appeal to another theorem Nov 7 asked How to prove Riemann integrable with partitions Nov 7 comment Squares of differentiable functions Sorry @dfeuer I meant $(f(x))^2$. Thanks Daniel Fischer! Nov 7 asked Squares of differentiable functions Nov 5 accepted Limit of metric of sequences Nov 5 comment Limit of metric of sequences Ah! I have seen it: $|\rho(x_n,y_n) - \rho(x,y_n)| \leq |\rho(x_n,x) + \rho(x,y_n) - \rho(x,y_n)|$ Nov 5 comment Limit of metric of sequences Hmm, in that case I suppose I'm just not quite sure how to show that something like $|\rho(x_n,y_n) - \rho(x, y_n)|$ can be made small? Nov 5 comment Limit of metric of sequences Ah yes I was unsure here whether I could use the absolute value metric $|\cdot|$ to prove convergence or whether I had to use a general $\rho$ to prove convergence. And $\rho$ is indeed a metric on $\mathbb R$