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5m
comment How to give a good guess to the recurrence relation problem
@BlediBoss take $p=1$, we only get a formula of $T(2n)$ for $n$ in form of $2^k$, but it's not for all $n$. For example I can define $T(2n+1) = e^{2n+1}$, of course it grows much faster than $n$ and $\log n$
24m
comment How to give a good guess to the recurrence relation problem
Your recurrence relation only defines a sequence $T(2^kp)$ for each $p$, and there is no relation between sequence with different $p$. But of course if you take $p=1$, you get a formula for $T(2^k)$
37m
answered How to give a good guess to the recurrence relation problem
55m
comment Prove that $(√3+2)^{m}$ is not a natural number for all natural numbers $m≥1$
You can show that $\{a + b\sqrt{3}, a, b \in \mathbb{N}^*\}$ is closed under multiplication
11h
reviewed Approve suggested edit on straightforward calculus problem
11h
comment How prove this Ratio Test and Its Generalizations problem?
nice +1! Btw, you forget the minus in the last inequality
12h
comment How to finish this proof about $\sigma$-algebras?
@G.T.R when I can find a such $C_n$, I mean $D_n = \Omega$, when I can find such a $D_n$, I take $C_n = \emptyset$. Then $y_n$ is not in $C_n^c \cap D_n$, but all $x_n$ are in it, isn't it?
22h
comment Prove that $\int_0^\infty \frac{\ln x}{x^n-1}\,dx = \left(\frac{\pi}{n\sin\left(\frac{\pi}{n}\right)}\right)^2$
Just to put @Lucian's comment clear, for non-experts like me, we define $f(k) = \int_0^\infty \dfrac{x^{k-1}}{1-x^n}dx$, then $f'(k) = \int_0^\infty \dfrac{ \log x x^{k-1}}{1-x^n}dx$, so the integral in question is $-f'(1)$
22h
comment How to finish this proof about $\sigma$-algebras?
@G.T.R Got your point, thanks. How about now? I've edited
22h
revised How to finish this proof about $\sigma$-algebras?
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23h
comment How to finish this proof about $\sigma$-algebras?
@G.T.R I think it's ok, unless I've missed something :). It's exactly but your definition of equivalence class that we can find such $C_n$, because if we can't find such $C_n$, then $y_n$ is in the equivalence class of $\{x_1, x_2, \cdots \}$
23h
comment Does $1-1+1/2-1/2+1/3-1/3+\cdots$ converges?
@Kun we have $S_{2n} = 1 - 1 + \frac{1}{2} - \frac{1}{2} + \cdots + \frac{1}{n} - \frac{1}{n} = 0$ and $S_{2n+1} = 1 - 1 + \frac{1}{2} - \frac{1}{2} + \cdots + \frac{1}{n} - \frac{1}{n} + \frac{1}{n+1} = \frac{1}{n+1}$
23h
answered proof T is a stopping time
23h
revised proof T is a stopping time
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23h
revised How to finish this proof about $\sigma$-algebras?
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23h
comment Does $1-1+1/2-1/2+1/3-1/3+\cdots$ converges?
@Kun, it's enough to compute directly by the definition of partial sum
23h
revised How to finish this proof about $\sigma$-algebras?
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1d
answered How to finish this proof about $\sigma$-algebras?
1d
revised Representing of natural number
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1d
answered Show that $\begin{align}{n \choose k}{k \choose m} = {n \choose m}{n-m \choose k-m}.\end{align}$