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Jul
30
reviewed Close Questions about Variance and Covariance
Jul
30
reviewed Close Help with binomial identity
Jul
30
reviewed Close Diophantine equation of four variables
Jul
30
reviewed Close Orbits of the tetrahedron
Jul
30
reviewed Close Injections, Surjections, Bijections
Jul
30
reviewed Close Integral $\int_{0}^{+\infty}\frac{t \sin(t)}{t^{2}+b^{2}}dt$
Jul
30
reviewed Close Hypercyclic Group
Jul
30
reviewed Close Continuous distribution and independence
Jul
30
accepted Periodic orbits of “even” perturbations of the differential system $x'=-y$, $y'=x$
Jul
30
comment Billingsley Exercise 8.8 (Markov Chains)
@NateEldredge Right, I was misleading, sorry about that.
Jul
29
revised Help solving integration: $I=\int_{-\infty}^{\infty}\phi\left(x\right)\Phi\left(a/\sqrt{b+c\mathrm{e}^{\frac{x-\mu}{\sigma}}}\right)dx$
deleted 6 characters in body; edited title
Jul
29
comment Limit and summation.
OK, let me do your job: what would be the limit of $$\sum_{i=1}^{n} \frac{1}{n^{4}+i+5}\ ?$$
Jul
29
comment Limit and summation.
Sure, I understood the first time, "the steps to get the final result". Which steps did you try? You would not dream of receiving a full solution having given no personal input whatsoever, would you? O no, I cannot believe you would.
Jul
29
comment Summation of infinite series, where difference in consecutive denominator forms an A.P.
"The elementary tool is the same " Actually no, not in general.
Jul
29
comment Limit and summation.
You are welcome. "But what about steps" You mean, your steps? Indeed, what about them?
Jul
29
comment Summation of infinite series, where difference in consecutive denominator forms an A.P.
The question specifies "for example".
Jul
29
comment Limit and summation.
At your service: $$\color{red}{\bf\frac74}$$ Note that the amount of explanations for this "solution" matches the amount of indications you gave about what you actually tried to solve this.
Jul
29
comment Limit and summation.
Riemann sums work excellently, what did you actually try?
Jul
29
comment How do i find formula for the recurrence relation :$x_{n+1}= x^2_{n}-x^2_{n-1}$ with :$x_{-1}=0,x_{0}=\frac{3}{4}$?
As said by others, finding a formula for $x_n$ is impossible and showing that $x_n\to0$ is direct.
Jul
29
comment Poincaré-Bendixson theorem, periodic solutions/periodic orbits
Imagine solutions in polar coordinates $(r(t),\theta(t))$ with $\theta(t)=t$ and $r(t)=1-(1-r_0)e^{-t}$, then, for $r_0\ne1$, the solution never meets the unit circle, is not periodic, and has the unit circle as limit set, and the limit set $r=1$ is indeed a periodic orbit.