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Feb
3
comment If $\sum x_n$ converges absolutely . I'll have to show that $\sum \frac{x_n }{1+ x_n} $ converges .
They may not be exactly the same as your question, but the approaches are applicable to this problem and your statement is proved in more or less the same fashion.
Feb
3
comment If $\sum x_n$ converges absolutely . I'll have to show that $\sum \frac{x_n }{1+ x_n} $ converges .
1] math.stackexchange.com/questions/708831/… 2] math.stackexchange.com/questions/1264577/… 3] math.stackexchange.com/questions/395292/… 4] math.stackexchange.com/questions/411280/…
Feb
2
comment Show that $\frac{1}{1+k}=\frac{\frac{1}{k}}{1+\frac{1}{k}}\leq \ln(1+\frac{1}{k})\leq\frac{1}{k}$
@JellyBelly math.stackexchange.com/questions/504663/…
Feb
2
revised Show that $\frac{1}{1+k}=\frac{\frac{1}{k}}{1+\frac{1}{k}}\leq \ln(1+\frac{1}{k})\leq\frac{1}{k}$
added 36 characters in body
Feb
1
answered Show that $\frac{1}{1+k}=\frac{\frac{1}{k}}{1+\frac{1}{k}}\leq \ln(1+\frac{1}{k})\leq\frac{1}{k}$
Jan
27
comment Derivative of trace of matrix product
cal.cs.illinois.edu/~johannes/research/matrix%20calculus.pdf
Jan
23
answered Finding $\sum_{k=1}^{\infty}k^2 \frac{2^{k-1}}{3^k}$
Jan
20
comment Solving SVM classifier with two weight vectors
@user2204324 Updated based on your recent edits.
Jan
20
revised Solving SVM classifier with two weight vectors
added 597 characters in body
Jan
20
comment Solving SVM classifier with two weight vectors
@user2204324 just updated the constraints as well.
Jan
20
revised Solving SVM classifier with two weight vectors
added 243 characters in body
Jan
20
answered Solving SVM classifier with two weight vectors
Jan
13
comment Prove that $\int_{2}^{\infty} \frac{dx}{x^{1-\epsilon}\cdot \ln(x)^{\beta}}$ diverges for every $\beta$.
Put $\ln x = y$. Should make your analysis easier.
Jan
13
comment Mutual Information Always Non-negative
@becko The same arguments hold, you just have to replace the summations by integrals.
Jan
11
answered How to prove $\cos \theta + \sin \theta =\sqrt{2} \cos\theta$.
Jan
9
revised Maximize $Ax^{m-1}(1-x)^{n-1} - Bx^{m-2}(1-x)^{n}$
edited title
Jan
9
comment Maximize $Ax^{m-1}(1-x)^{n-1} - Bx^{m-2}(1-x)^{n}$
@AlexR. I have added the gradient to the original post.
Jan
9
revised Maximize $Ax^{m-1}(1-x)^{n-1} - Bx^{m-2}(1-x)^{n}$
added 460 characters in body
Jan
9
comment Maximize $Ax^{m-1}(1-x)^{n-1} - Bx^{m-2}(1-x)^{n}$
Whosoever downvoted the question, please at the very least give an explanation for your downvote. Otherwise, you are just being ridiculous.
Jan
9
comment Maximize $Ax^{m-1}(1-x)^{n-1} - Bx^{m-2}(1-x)^{n}$
@AlexR. Ok, I am looking to give an analytical expression for arg max in terms of $c,m, n$. Secondly, if you look at the optimization problem, my x is constrained in [0, 1]. However, if we differentiate and set to 0, we are doing unconstrained optimization. So, the natural question here is why must the roots of the quadratic lie in [0, 1] always for all $c,m,n$?