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2d
comment Find the interval of convergence $\displaystyle \sum_{n=1}^\infty \dfrac{(3n)!(x^n)}{(n!)^3}$
Well, weak approximations like $(n/4)^n\le n!\le (n/2)^n$ do not work for sure..
2d
revised Find the interval of convergence $\displaystyle \sum_{n=1}^\infty \dfrac{(3n)!(x^n)}{(n!)^3}$
deleted 9 characters in body
2d
answered Find the interval of convergence $\displaystyle \sum_{n=1}^\infty \dfrac{(3n)!(x^n)}{(n!)^3}$
Apr
30
revised Smallest distance of a point to a surface
edited title
Apr
30
comment Can we find prime numbers with any sum of digits (except those divisible by three)
I couldn't even consider it a heuristic..
Apr
30
revised Smallest distance of a point to a surface
added 10 characters in body; edited title
Apr
30
comment Smallest distance of a point to a surface
You're right; anyway, apart from relabelings, the question should be clear enough
Apr
30
comment Smallest distance of a point to a surface
Indeed no, it is as if everything has been defined on $\mathbf{R}^{n-1}$
Apr
30
asked Smallest distance of a point to a surface
Mar
29
comment Minimum of $\sum \left|7x-1\right|$
Well, I did know this pretty manual solution; but isn't any better option?
Mar
29
comment Prove the following Theorem. For all positive integers n, some element of the set {n, n + 1} is divisible by 2.
Come on, such a question shouldn't have been posted
Mar
29
revised Prove the following Theorem. For all positive integers n, some element of the set {n, n + 1} is divisible by 2.
added 104 characters in body
Mar
29
revised Transformation of positive semi-definite matrices
deleted 130 characters in body
Mar
29
answered Prove the following Theorem. For all positive integers n, some element of the set {n, n + 1} is divisible by 2.
Mar
28
revised Transformation of positive semi-definite matrices
added 134 characters in body
Mar
28
comment Transformation of positive semi-definite matrices
Which limit are you talking about? Consider the matrix X=[1,2,2; 2,1,1; 2,1,1]. Then the determinants of $X_{123}$, $X_{23}$ and $X_3$ are nonnegative. But $X$ is not PSD.
Mar
28
comment Transformation of positive semi-definite matrices
A matrix $M$ is positive semi-definite if $x^TMx$ is nonnegative for each vector $x$. On the other hand, positive definiteness require strictly positiveness. The version of Sylvester criterion which you are talking about is about the latter case. Of course, there are variants of such criterion also for PSD matrices, but probably your condition is not sufficient. [I am just aware of a version requiring to check all principal minors, which is not quoted in Wikipedia]
Mar
28
comment Transformation of positive semi-definite matrices
Indeed, here we are not talking about positive definite matrices.
Mar
28
comment Transformation of positive semi-definite matrices
Where did you take such version of Sylvester criterion about positive semi-definite matrices? I believe too the answer is affirmative, but shouldn't we check all principal minors of $A$ and $B$? ..
Mar
28
asked Transformation of positive semi-definite matrices