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 May22 answered Question about a proof that $\mathbb{Q}$ is dense in $\mathbb{R}$ May21 comment How to calculate this multi-integral? The sign is wrong. The last integral should be +1/2 sin(z). May4 comment prove this inequality$1+x+\dfrac{x^2}{2!}+\dfrac{x^3}{3!}+\cdots+\dfrac{x^n}{n!}>\dfrac{e^x}{2}$ @math110, it is the same. You only need to show $n! > 2e^{-\lambda n} \int^{\lambda n}_0 (\lambda n -t)^n e^t dt$ which follows basically what you have already. May4 comment prove this inequality$1+x+\dfrac{x^2}{2!}+\dfrac{x^3}{3!}+\cdots+\dfrac{x^n}{n!}>\dfrac{e^x}{2}$ @math110, I meant replace your argument of $x=n$ with $x=\lambda n$ and you will arrive at the same conclusion you have for $x=n$. May4 comment prove this inequality$1+x+\dfrac{x^2}{2!}+\dfrac{x^3}{3!}+\cdots+\dfrac{x^n}{n!}>\dfrac{e^x}{2}$ I think you can do this by letting $x := \lambda n$ where $0 \lt \lambda \le 1$. All your inequalities will remain true. Jan16 comment Lost on algebra notation @Clayton, I think that's an exaggeration. Most undergrad number theory books don't require much algebra prerequisites if any (eg, old books like Landau and Hardy/Wright). Dec24 comment Proving that $\left(1+\frac{z_{1}}{z_{2}}\right)\left(1+\frac{z_{2}}{z_{3}}\right)…\left(1+\frac{z_{n}}{z_{1}}\right)\in\mathbb R$ should be 2\cos(t_i-t_j)e^(i(t_i-t_j))? Sep19 comment Limit of an integral containing a product Are the integral limits 1 to infinity and do you mean N approaches infinity instead of of x? Mar30 comment If a rational number has a finite decimal representation, then it has a finite representation in base $b$ for any $b>1?$ Not true. 0.1 base 10 = 0.00011001100110011.... in base 2. Mar28 answered Real Analysis Book Choice Mar24 comment How can I use Cauchy integral formula for this integral $g(z)=\int_{C}\frac{s^2+s+1}{s-z}ds$? Also you should remember if f(z)/(z-z_0) is analytic within and on C, then the integral is 0. Mar12 comment Chernoff bounds - basic results One question: did you check the Wikipedia article on Chernoff Bound? Mar1 comment Statistics resources with examples for a C.S. student He wants statistics resources not probability. Feb27 awarded Yearling Feb19 answered Mathematical function for the powers Jan28 comment Conditional expectation of $E[X|Z]$ where $Z= \max(X,Y)$ @Didier Piau, thanks for the clarification! For some reason I had always thought $;$ or $|$ meant the same thing; similar to $:$ and $|$ for describing sets. Jan28 comment Conditional expectation of $E[X|Z]$ where $Z= \max(X,Y)$ @Didier Piau, I don't understand why the numerator isn't $zf_X(z)F_Y(z) + \mathbb{E}(X|X \le z)f_Y(z)F_X(z)$. Jan22 comment Real life applications of Topology Knowledge of topology is often crucial for passing your PhD qualifying exams in math. You do want your PhD, don't you? Jan20 comment find the distribution of $Z = Y\sqrt X$ Is it truly $V_1/V_2$ and $V_2$? If so then yes. Jan19 revised Which of these two ways to take the derivative of a delta function times another function is correct? \delta(x)f'(x) not \delta'(x)f(x)