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 Mar17 awarded Yearling Feb9 comment Prove that $\sum_{n=1}^{\infty}\frac{|\cos n|}{n}$ diverges I have seen this three times in this website, I answered it one time. You can search my profile for an answer. Feb7 comment $\zeta_m(s)=\prod\limits_{p\nmid m} \frac{1}{\left(1-\frac{1}{p^{f(p)s}}\right)^{g(p)}}$ is a Dirichlet series with non-negative coefficients Use $1/(1-x)= 1+ x + x^2 + \cdots$ and multiply it through. Jan29 comment probablity - $n$ previolusly persons failed exam ( extremely difficult) It looks like $\sum_{i=0}^{k-1}P(A|N_i)P(N_i)$ cannot exceed $1$. So, I think it is $k=1$. Jan12 comment How prove there exsit $M$ such $a_{n}\le M$ Maybe using the graph of $y=(\sqrt{x} + x)^{1/3}$ works. Dec6 comment Negative binomial distribution - sum of two random variables If $X\sim NB(r,p)$, then $X=k$ means $k$ is the time of $r$-th success. The geometric random variable gives the first time of success. Dec6 answered Negative binomial distribution - sum of two random variables Nov30 comment Prove that $AA^T=0\implies A = 0$ Your problems on title and the content are different. Nov26 comment Asymptotics for the Alternating Mertens Function So, for any $K>0$, it is bounded above by $n/(\log n)^K$. Nov26 comment Asymptotics for the Alternating Mertens Function Nov13 comment Limit of the sequence $(\sin n)^{n}$ $(\sin n)^{n^2}$ diverges as well. Nov3 comment If $\mathrm{E} |X|^2$ exists, then $\mathrm{E} X$ also exists Why do you use Jensen's inequality, what about Cauchy-Schwarz? Oct15 comment $P(AB=BA)$ , $A,B\in M_{3x3}(\mathbb Z/p\mathbb Z)$ They are THE solutions only if the minimal polynomial of $A$ coincides with the characteristic polynomial. Oct13 awarded Nice Answer Oct9 comment An exotic sequence I now see that your solution implies that the irrational number (it might be even transcendental) $\arctan(\sqrt 7 )/\pi$ has a finite irrationality measure. Oct8 comment An exotic sequence I see. The last line is essentially from $\sin x \sim x$, right?. Oct8 comment An exotic sequence I think the last line should be $|\arg a^k \pm i\pi/2| > (\textrm{constant}\cdot k)^{-\mu}$. Oct8 comment Show $\sum_n \left(1-\frac{K}{n^{1-\epsilon}\sqrt{\log n}} \right)^n$ converges for $\epsilon>0$. Comparison test. Oct7 comment An exotic sequence That number $2\arctan(\sqrt 7 )/\pi$ is an irrational number. Oct7 comment Proving that $\left|\Re\left( \frac{1+i\sqrt{7}}{2}\right)^n\right| \to \infty$ I tried proving this with SML by myself. Even with SML, it is difficult.