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How to deduce if series is convergent (depending on parameter $a$):$$sum_{n=1}^inftyleft[left(1+frac{1}{n}right)^{n+1}-aright]sin{n}?$$ If $a=e,$ we have that $lim_{ntoinfty}a_n=0,$ but it is not sufficient to...
Asked on 12/09/2020 by alans
1 answerI notice that in a lot of linear transformation proofs involves making assumptions about mapping a basis vector to another basis vector or to 0. I was wondering why this...
Asked on 12/09/2020
3 answerSuppose, I have two random variables $X$ and $Y$. Both of them can produce output 0 and 1. Variable $X$ has the probability of emitting 1 is...
Asked on 12/09/2020 by Buyanov Igor
1 answerWhere can I find literature on why the choice of regularization $$int_{Omega} |nabla u| ,{rm d} x,{rm d}y$$ is more effective than the classical choice $$int_{Omega} |nabla...
Asked on 12/09/2020 by Pazu
1 answerWe know the binomial expansion of $(1+x)^n$ when $n$ is a fractional index or negative index. Why can we not expand $(a+b)^n$ directly when $n$ is...
Asked on 12/08/2020
1 answerLet $A, B$ be skew-symmetric matrices such that $AB = -BA$. Show that $AB = 0$.I know that $AB$ is skew-symmetric,because $$(AB)^t=B^tA^t=BA=-AB$$but I...
Asked on 12/08/2020 by Carlos Andres Henao Acevedo
1 answerI am currently doing some practice problems for the analysis qual. I have some thoughts on the following problem, and it would be great if someone could see if I...
Asked on 12/08/2020 by Kevin_H
1 answer$$ int _ 0 ^ { + infty } frac 1 { sqrt { 1 + x ^ 8 } } mathrm d x $$I have a hint...
Asked on 12/08/2020 by Sandro Gakharia
4 answerUsing the multinomial theorem$$ left(sum_{j=1}^{N} x_j right)^N = sum_{m_1 + cdots + m_n = N} frac{N!}{m_1! cdots m_N!} x^{m_1} cdots x^{m_N}, $$and the contour integral expression of...
Asked on 12/08/2020 by motherboard
0 answerLet $X_{1}, ldots, X_{n}$ be a sample from the distribution $mathrm{N}(mu, 1)$ and consider testing $H_{0}: mu=mu_{0}$ versus $H_{1}: mu=mu_{1}$ where $mu_{0}<mu_{1}$ are known numbers....
Asked on 12/08/2020 by Hachiman Hikigaya
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