M. Strochyk
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 Mar 15 comment Formula for the summation of the series $a+2a^2+3a^3+…$ upto nth term? After differentiation it's easy to code it. Mar 15 revised Formula for the summation of the series $a+2a^2+3a^3+…$ upto nth term? added 61 characters in body Mar 15 revised Formula for the summation of the series $a+2a^2+3a^3+…$ upto nth term? added 61 characters in body Mar 15 answered Formula for the summation of the series $a+2a^2+3a^3+…$ upto nth term? Mar 14 revised How to solve $\cos(x)\cos(2x)\cos(4x)=1/8$ added 87 characters in body Mar 14 answered How to solve $\cos(x)\cos(2x)\cos(4x)=1/8$ Mar 14 comment Help finding $\lim_{x \to \infty} {(1 + e^x)}^{e^{-x}}$ If $\ln{L}=0$ then $L=?$ Mar 11 answered Multivariable partial differentiation Mar 3 reviewed Reject Investment in simple interest Feb 10 comment Writing a function $f : [-\pi,\pi) \to \mathbb{R}$ as $\sum c_k e^{ikx}$ where $c_k$ is to be found $c_k=\frac{1}{2\pi}\int\limits_{-\pi}^{\pi}{f(x)e^{ikx}\,dx} = \frac{1}{2\pi}\int\limits_{-\pi}^{0}{(-1)\cdot e^{ikx}\,dx}+\frac{1}{2\pi}\int\limits_{0}^{\pi}{1\cdot e^{ikx}\,dx}.$ Feb 10 comment Sum and radius of $\sum_{n=0}^{\infty}(\cos(5n)+i \sin(5n))z^{n}$ $|e^{i \varphi}|=1$ for all $\varphi \in \mathbb{R}.$ Feb 10 answered To evaluate $\lim_{x \to 0^+} \frac{\log(x)}{\sqrt x}$ using inequality Feb 6 revised Evaluate the definite integral $\int_{0}^{a}\frac{dx}{(a^2+x^2)^{3/2}}$ Markdown Feb 6 comment Evaluate the definite integral $\int_{0}^{a}\frac{dx}{(a^2+x^2)^{3/2}}$ Hint: Try using substitution $x=a\sinh{t}.$ Feb 3 comment $z^n=(i+z)^n$, solve for $z$ If $z=r(\cos{\varphi}+i\sin{\varphi})$ then $1+z=(1+r\cos{\varphi})+ir\sin{\varphi}.$ Jan 22 comment Showing convergence of the integral $\int_{1}^{\infty}\frac{\ln(x)\cos(x)}{x^2+1}\,{\rm d}x$ Hint: For an arbitrary fixed $\varepsilon>0 \ \lim\limits_{x\to\infty}{\frac{\ln{x}}{x^\varepsilon}}=0,$ which imply $\ln{x} < x^\varepsilon$ for all $x > x_\varepsilon.$ Jan 21 answered I would like to calculate limit: $\lim_{n \to \infty}{n\cdot \ln({1-\arctan{\frac{3}{n}}})}$ Jan 20 reviewed Approve Proof of $a^{\frac{p-1}{2}} \equiv \left(\frac{a}{p}\right)$ mod $p$ Jan 20 comment Reducing a particular fraction $\frac{t-1}{t} =1-\frac{1}{t}$ Jan 20 comment Determine if this power series is convergent for Z on the boundary of it's disc of convergence Since the radius of convergence $R=2,$ then for each point on the boundary of disc of convergence we have $z+2i=2e^{i\varphi}.$ Thus for these points $$(1+i\sqrt{3})\sum\limits_{n=0}^{\infty}{\dfrac{1}{n^2 2^n}(z+2i)^n}=(1+i\sqrt{3})\sum\limits_{n=0}^{\infty}{\dfrac{2^n e^{in\varphi}}{n^2 2^n}}=(1+i\sqrt{3})\sum\limits_{n=0}^{\infty}{\dfrac{ e^{in\varphi}}{n^2}},$$ and the last series is absolutely convergent.