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 Oct10 comment Does this sum go to 0? Of course I could be wrong. It indeed might not go to 0. But that means I wasted another half a day on this problem. Oct10 comment Does this sum go to 0? @process91, think about this sum, $\sum_{k=1}^{\lceil n/2 \rceil} (1-p)^{k(n-k)}$. Erdos has proved it goes to 0, if $p = c \log n / n, c > 1$. I'm actually trying to mimic what he did : renyi.hu/~p_erdos/1961-15.pdf Oct10 comment Does this sum go to 0? I'm taking a course of random graph. The exercises are really difficult. Sometimes no students in class could solve all of them. These equations are the best I can reach. If I can get $S \to 0$ then I'm done. But I've completely no idea if this is the correct direction or it's a just another dead end. Oct10 asked Does this sum go to 0? Oct10 accepted What's the lower bound of the sum $S(n) = \sum_{k=1}^n \prod_{j=1}^k(1-\frac j n)$? Oct10 comment What's the lower bound of the sum $S(n) = \sum_{k=1}^n \prod_{j=1}^k(1-\frac j n)$? Oh yeah, I should be more careful about typos. Oct10 revised What's the lower bound of the sum $S(n) = \sum_{k=1}^n \prod_{j=1}^k(1-\frac j n)$? edited body Oct10 asked What's the lower bound of the sum $S(n) = \sum_{k=1}^n \prod_{j=1}^k(1-\frac j n)$? Oct10 comment What's the asymptotic lower bound of the sum $\frac 3 2 + \sum_{k=3}^{n} \frac{n!}{k(n-k)!n^k}$? That's really impressive. Oct10 accepted What's the asymptotic lower bound of the sum $\frac 3 2 + \sum_{k=3}^{n} \frac{n!}{k(n-k)!n^k}$? Oct10 comment What's the asymptotic lower bound of the sum $\frac 3 2 + \sum_{k=3}^{n} \frac{n!}{k(n-k)!n^k}$? The 2 $(n-2)$ is a typo, I just fixed it. Oct10 revised What's the asymptotic lower bound of the sum $\frac 3 2 + \sum_{k=3}^{n} \frac{n!}{k(n-k)!n^k}$? edited body Oct10 asked What's the asymptotic lower bound of the sum $\frac 3 2 + \sum_{k=3}^{n} \frac{n!}{k(n-k)!n^k}$? Oct8 revised Given a random graph $G_{n,p}$, how to get the expectation of number of components with $k$ vertices and $k$ edges? edited title Oct8 asked Given a random graph $G_{n,p}$, how to get the expectation of number of components with $k$ vertices and $k$ edges? Oct2 accepted Does this sum have an upper bound? Oct2 comment Does this sum have an upper bound? Oh, that answered my question, thx! Oct2 asked Does this sum have an upper bound? Oct2 comment Is it possible to get the coefficients of the power series No, I can't, although the problem doesn't indicate the domain of s explicitly, in the context, $s$ is a real number. Oct1 accepted Is it possible to get the coefficients of the power series