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 Feb1 comment Properties of sup and lim inf. @Vinith I think you should not accept such a quick answer. Unless, of course, you've already checked my tip step by step with pencil and paper. Dealing with 'sup' and 'inf' it is necessary familiarity and a good understanding the definition of supremum and the definition of infimum. This familiarity is achieved with practice various exercises. Feb1 revised Properties of sup and lim inf. added 13 characters in body; edited title Feb1 revised Properties of sup and lim inf. added 137 characters in body Feb1 answered Properties of sup and lim inf. Feb1 revised $\sum_{n=1}^{\infty}a_{n}$ diverges but $\sum_{n=1}^{\infty}\frac{a_{n}}{1+a_{n}^{2}}$ sometimes converges and sometime diverges. added 7 characters in body Jan31 reviewed Approve Compute the Frobenius norm Jan31 comment Proof by induction: $(1+x)^n > 1 + nx+nx^2$ @Mufasa Note that if we use approach Taylor (or binomial approximation by Newton) combined with the principle of mathematical induction we get demonstration in which the principle of mathematical induction is superfluous. Jan31 revised $\sum_{n=1}^{\infty}a_{n}$ diverges but $\sum_{n=1}^{\infty}\frac{a_{n}}{1+a_{n}^{2}}$ sometimes converges and sometime diverges. deleted 21 characters in body Jan31 revised $\sum_{n=1}^{\infty}a_{n}$ diverges but $\sum_{n=1}^{\infty}\frac{a_{n}}{1+a_{n}^{2}}$ sometimes converges and sometime diverges. added 67 characters in body Jan31 answered $\sum_{n=1}^{\infty}a_{n}$ diverges but $\sum_{n=1}^{\infty}\frac{a_{n}}{1+a_{n}^{2}}$ sometimes converges and sometime diverges. Jan24 revised Help with integration of $\frac{f'(x)}{[f(x)]^n}$. edited title Jan23 revised Find this limit: $\lim_{n \to \infty}{(e^{\frac{1}{n}} - \frac{2}{n})^n}$ edited tags Jan23 awarded Good Answer Jan22 revised convergence of $\prod_{n=1}^\infty (1-\frac{z}{n!})$ edited tags Jan18 awarded Popular Question Jan17 reviewed Close Simplifying a hyperbolic trigonometric expression Jan17 reviewed Close let $x$ be in finite group $G$ and let order of $x$ is $p$. If $h^{-1}xh = x^{10}$ for a finite group show that $p=3$ Jan15 comment convergence of $\prod_{n=1}^\infty (1-\frac{z}{n!})$ @corciacandy What do you mean by 'order'? If you are talking about convergence order towards the convergence of the product is uniform or punctually you can use the M test Weiersstrass to achieve uniform convergence. Jan13 revised convergence of $\prod_{n=1}^\infty (1-\frac{z}{n!})$ added 534 characters in body Jan13 answered convergence of $\prod_{n=1}^\infty (1-\frac{z}{n!})$