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Undergraduate at University of Lund, Mathematics


9h
comment Proving a matrix is always symmetric
We say that a square matrix A is symmetric if $A^{t}=A$ where $A^{t}$ denotes the transpose of A. You should look up the definitions more carefully.
9h
answered Proving a matrix is always symmetric
1d
awarded  Yearling
Sep
13
comment prove that $(E_{p^n},*)$ is cyclic group
It suffies to prove that each primepower has a primitive root, and that will be your candidate as the generater of the group
Sep
13
comment How to show this integral equals $\pi^2$?
Yes, I noticed that! Since you where a few minutes earlier than me I gave you a thumbs up! :)
Sep
13
answered How to show this integral equals $\pi^2$?
Sep
12
answered Find $ \lim\limits_{x \to 0^+}x\int_x^1 \dfrac{\cos t}{t^2}\hspace{1mm}dt$
Aug
19
comment For an irrational number $a$ the fractional part of $na$ for $n\in\mathbb N$ is dense in $[0,1]$
It follows from the fact that the points of an equidistributed sequence of an arbitrary interval [a,b] form a dense subset of [a,b].
Jul
5
comment Evaluation of $\int_0^1 \frac{\log(1+x)}{1+x}\log\left(\log\left(\frac{1}{x}\right)\right) \ dx$
Have you tried the sub. $\log(\frac{1}{x})=t$
Jul
1
comment Integrating a series
Lopk up Beppe Levi's Theorem
Jul
1
comment Does $\sum\limits_{n=1}^\infty \left[n\left(f\left(\frac{1}{n}\right)-f\left(-\frac{1}{n}\right)\right)-2f'(0)\right]$ converge?
Mean-Value theorem?
Jul
1
comment Proof $(\frac{n+1}{n})^n>2$ for positive $n$
Look up Bernoullis inequality!
Jul
1
answered A series converging (or not) to $\ln 2$
Jun
26
answered Integrate $1/(x^5+1) $from $0$ to $\infty$?
Jun
25
awarded  Necromancer
Jun
25
comment how to prove $f(t)\rightarrow L$ as $t\rightarrow \infty$
Hint: Do an integration by parts on $$\frac{1}{T}\int_{0}^{T}f(t)dt$$
Jun
23
comment The limit of $f(x,y)=\sum_{n=1}^\infty \frac{x}{x^2+yn^2}$ as $x\to \infty$.
If I am not mistaken the series is Riemannsum. $$\sum_{n=1}^{\infty}\frac{1}{x}\frac{1}{1+y(\frac{n}{x})^{2}}\rightarrow \int_{0}^{\infty}\frac{dt}{1+yt^{2}}$$ as $x\rightarrow \infty$
Jun
23
answered How to prove $ \lim_{n \to \infty} e^n \cdot \left( \sum_{k=0}^{n-1} ({k-n \over e})^k/k! \right)- 2 \cdot n = \frac 23$?
Jun
20
comment Show that $\lim_{n\rightarrow \infty} \int_0^{\pi/2} 2^n \sqrt{n} \sin^n(x) \cos^{n-2}(x) \; dx = \sqrt{2\pi}$
Indeed it does. We actually get nice things to work with since the expression simplifies to $$2^{2n}\sqrt{2n+1}\frac{\Gamma(n)\Gamma(n+1)}{\Gamma(2n+1)}$$
Jun
19
comment Prove that $\sigma_k$ is a multiplicative function
Seems legit to me!