1,546 reputation
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bio website cse.iitb.ac.in/~aruniyer
location India
age 30
visits member for 2 years, 4 months
seen yesterday

Aug
4
comment Prove that $e^{\sum 1/p_k^2} > \pi/2$
(+1) for your answer. And it was my answer that used Prime Zeta Function and it wasn't correct, so I retracted it before it got any undeserved attention -_-; sheepish grin
Aug
4
comment Prove that $e^{\sum 1/p_k^2} > \pi/2$
Yes, realized that a while ago. Proving things without sleep is a bad idea.
Aug
4
answered Prove that $e^{\sum 1/p_k^2} > \pi/2$
Aug
1
comment Prove: $\int_0^{\infty}\left(\frac{\sin x}{x}\right)^2dx=\pi/2$
@PeterTamaroff is correct (+1). Put $\delta = \frac{1}{m}$ for some $m$. What does that give you?
Jul
31
comment Prove: $\frac{1}{1^2} +\frac{1}{2^2} + \cdots + \frac{1}{n^2} + \cdots = \sum_{n=1}^\infty \frac{1}{n^2} < 2$
@BarryCipra Agreed.
Jul
31
comment Prove: $\frac{1}{1^2} +\frac{1}{2^2} + \cdots + \frac{1}{n^2} + \cdots = \sum_{n=1}^\infty \frac{1}{n^2} < 2$
+1 Shouldn't that be <= because it is equal for n = 1?
Jul
29
comment A minimization problem
Taking derivative gives $w - u + 2\beta\frac{w}{x^{\circ 2}}$ and second derivative is semi-definite. Therefore, setting the derivative to zero should give you a local minimum.
Jul
29
comment Find the sum : $\sin^{-1}\frac{1}{\sqrt{2}}+\sin^{-1}\frac{\sqrt{2}-1}{\sqrt{6}}+\sin^{-1}\frac{\sqrt{3}-\sqrt{2}}{\sqrt{12}}+\cdots$
+1 This is a very beautiful answer!
Jul
29
revised Show if $\|\cdot\|$ is a norm then $\|f(\cdot)\|$ is a norm where $f$ is linear and invertible
Minor correction to notation
Jul
29
suggested suggested edit on Show if $\|\cdot\|$ is a norm then $\|f(\cdot)\|$ is a norm where $f$ is linear and invertible
Jul
27
revised show that $\int_{0}^{\infty} \frac {\sin^3(x)}{x^3}dx=\frac{3\pi}{8}$
added 95 characters in body
Jul
27
answered show that $\int_{0}^{\infty} \frac {\sin^3(x)}{x^3}dx=\frac{3\pi}{8}$
Jul
26
comment $\lim_{x \to 1} \frac{x + x^2 + \dots + x^n - n}{x - 1} = \frac{n(n + 1)}{2}$
@EugeneBulkin True. I apologize for the confusion caused.
Jul
25
comment $\lim_{x \to 1} \frac{x + x^2 + \dots + x^n - n}{x - 1} = \frac{n(n + 1)}{2}$
Your definition of f(x) should not contain that n.
Jul
23
comment Given $\{\log_ab \mid a,b\in \mathbb N, \mathrm{gcd}(a,b)=1,a,b≥3\}$ does the sum of any two $\log_ab$ form an irrational or rational number?
Try verifying the conditions for the group. Is it closed? Is it associative? Does it have an identity? What about inverses?
Jul
23
accepted What is a set function that returns another set of points called?
Jul
22
revised Prove that $\gcd(x, y)=\gcd(x,ax+y)$, would this be the correct reasoning?
Minor corrections.
Jul
22
suggested suggested edit on Prove that $\gcd(x, y)=\gcd(x,ax+y)$, would this be the correct reasoning?
Jul
22
comment What is a set function that returns another set of points called?
Actually, hmm scratch that, possibly m can be fixed. I will have to think about it. Thanks! I will upvote for the moment, will accept once I get some clarity on the situation myself.
Jul
22
comment What is a set function that returns another set of points called?
The reason I used the word set is because the size m of S is not necessarily fixed.