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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.