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| bio | website | |
|---|---|---|
| location | ||
| age | ||
| visits | member for | 4 months |
| seen | yesterday | |
| stats | profile views | 69 |
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May 12 |
comment |
How to prove $(\frac{n+1}{e})^n<n!<e(\frac{n+1}{e})^{n+1}$ without integrating method? Though I guess you could argue that these inequalities are proven by integrating |
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May 12 |
answered | How to prove $(\frac{n+1}{e})^n<n!<e(\frac{n+1}{e})^{n+1}$ without integrating method? |
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May 8 |
revised |
Expected Value with Variable Probability added 250 characters in body |
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May 7 |
comment |
Linear Algebra and the determinant of matrix variation Write $M+\delta M = M(I + M^{-1}\delta M).$ |
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May 7 |
awarded | Caucus |
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May 7 |
comment |
Expected Value with Variable Probability I don't understand what you mean? I was just giving faulty reasoning. The nicest proof that I know is as follows: $E[X] = \frac{1}{p} \cdot 1 + \frac{p-1}{p} (E[X] + 1),$ whence $E[X] = \frac{1}{p}.$ |
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May 6 |
comment |
limit, low or high bound, convergence for recursive sequence in response to my previous post, of course you're right - how silly of me. |
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May 6 |
comment |
Expected number of turns what is the probability that it takes $k$ tries, for $1 \le k \le n$? |
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May 6 |
answered | Show that an orthogonal group is a $\frac{n(n−1)]}2-$dim. $C^\infty$-Manifold and find its tangent space |
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May 6 |
comment |
Problem related with the zeroes of a polynomial @learner I posted the proof yesterday |
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May 6 |
answered | Lebesgue integrable function and square-integrable functions? |
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May 6 |
comment |
Subsequence proof Did you see my comment above? The idea is that you want $a_n$ to be close to $b$ but far from $c.$ If $|a_n - b| < \epsilon,$ then $|a_n - c| \ge |b-c| - |b-a_n|$ by the triangle inequality. So taking $\epsilon$ as anything less than $|b-c|$ will get you some sort of lower bound on $|a_n - c|.$ He chose $\epsilon < |b-c|/2$ just because it's in the middle |
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May 6 |
comment |
Subsequence proof ah sorry about that; my reading abilities are lacking. Okay - think about what it means for $a_n$ to not converge to $c.$ This means that there exists $\epsilon$ and an (increasing) sequence $N_k$ such that $|a_{N_k} - c| \ge \epsilon.$ How would you draw this conclusion from what you're given? |
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May 6 |
comment |
Subsequence proof well, go for contradiction and use the definition of convergence |
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May 6 |
comment |
Induction proof: $\dbinom{2n}{n}=\dfrac{(2n)!}{n!n!}$ is an integer. this is a little unsatisfying because of that assumption, though |
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May 6 |
answered | Induction proof: $\dbinom{2n}{n}=\dfrac{(2n)!}{n!n!}$ is an integer. |
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May 5 |
comment |
What does the Heine-Borel Theorem mean? why is $(a,b)$ necessarily in $I$? |
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May 5 |
revised |
Problem related with the zeroes of a polynomial Added proof of theorem |
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May 5 |
answered | Problem related with the zeroes of a polynomial |
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May 5 |
revised |
Expected Value with Variable Probability added 1 characters in body |
