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visits member for 2 years, 4 months
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Jan
18
awarded  Fanatic
Jan
13
asked Continuity of the dual product reloaded
Jan
13
comment Is my proof that if $x_n$ is a sequence such that $x_n \rightarrow +\infty$ then $(1+\frac{1}{x_n})^{x_n}\rightarrow e$ correct?
Is $x_n$ an integer?
Jan
12
comment Is my proof that if $x_n$ is a sequence such that $x_n \rightarrow +\infty$ then $(1+\frac{1}{x_n})^{x_n}\rightarrow e$ correct?
Your solution is not correct. Maybe take a look at how you prove that $(1+1/n)^n\to e$ and try from there.
Jan
11
awarded  Yearling
Jan
11
comment Is the biconjugate of a continuous functions also continuous?
@Quickbeam2k1 I was talking about $f^{**}$ which can be identically $-\infty$. You still have to show that $f^{**}$ is proper. Convex Analysis by R.T. Rockafellar Theorem 10.1 p.82 has the finite dimensional case.
Jan
10
accepted Continuity of the dual product
Jan
10
comment Is the biconjugate of a continuous functions also continuous?
@Quickbeam2k1 The answer to both questions is negative. Convex functions are continuous on the interior of their domain if they are bounded above on an open subset of their domain (that holds in any space). Boundedness from above has nothing to do with proving that the function is proper because it can be identically $-\infty$.
Jan
10
comment Continuity of the dual product
another thing that requires a proof is that $n_i\to\infty$ but other than that the proof is OK
Jan
10
answered Is the biconjugate of a continuous functions also continuous?
Jan
9
comment Does $\sum_{n = 2}^{\infty} \frac{\sqrt{n + 1}}{n(n-1)}$ converge or diverge?
@user1176201 I will not write the general method since I find it trivial. But you should try it and if you have a problem with the limit computation try force factoring
Jan
9
comment Continuity of the dual product
the interesting part of your proof is missing, namely that $0$ belongs to the weak closure of $B$
Jan
9
comment Does $\sum_{n = 2}^{\infty} \frac{\sqrt{n + 1}}{n(n-1)}$ converge or diverge?
the power of $n$ on top minus the power of $n$ on the bottom (it's a general method).
Jan
9
comment Does $\sum_{n = 2}^{\infty} \frac{\sqrt{n + 1}}{n(n-1)}$ converge or diverge?
Limit Comparison with $1/n^{3/2}$ works
Jan
9
asked Continuity of the dual product
Jan
8
answered Why do you reject negative base solution for Logs?
Jan
7
answered Sufficient condition for convexity
Dec
22
comment Power series for the rational function $(1+x)^3/(1-x)^3$
Start with the geometric series and use operations like term-wise differentiation and multiplication by x.
Dec
19
awarded  Constituent
Dec
18
accepted Segment ordered density conjecture.