User Srivatsan

133 votes

Accepted

Check if a point is within an ellipse

answered Oct 27, 2011 at 20:20

65 votes

Accepted

A "fast" way for computing $ \prod \limits_{i=1}^{45}(1+\tan i^\circ) $?

answered Oct 25, 2011 at 19:30

51 votes

Accepted

Proving : $ \bigl(1+\frac{1}{n+1}\bigr)^{n+1} \gt (1+\frac{1}{n})^{n} $

answered Sep 15, 2011 at 19:12

50 votes

Accepted

What is your favorite application of the Pigeonhole Principle?

answered Sep 7, 2011 at 15:38

36 votes

Integral: $\int_{-\infty}^{\infty} x^2 e^{-x^2}\mathrm dx$

answered Sep 20, 2011 at 14:52

35 votes

Accepted

What are the rules for equals signs with big-O and little-o?

answered Nov 27, 2011 at 17:22

32 votes

Prove $\epsilon$-$\delta$ definition of continuity implies the open set definition for real function

answered Nov 28, 2011 at 1:42

28 votes

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Inequality involving $\limsup$ and $\liminf$: $ \liminf(a_{n+1}/a_n) \le \liminf a_n^{1/n} \le \limsup a_n^{1/n} \le \limsup(a_{n+1}/a_n)$

answered Oct 2, 2011 at 23:51

27 votes

What is your favorite application of the Pigeonhole Principle?

answered Sep 7, 2011 at 17:30

27 votes

Drunkard's walk on the $n^{th}$ roots of unity.

answered Jan 15, 2012 at 22:03

23 votes

Accepted

How does backwards induction work to prove a property for all naturals?

answered Jan 8, 2012 at 11:29

22 votes

Nested Square Roots $5^0+\sqrt{5^1+\sqrt{5^2+\sqrt{5^4+\sqrt\dots}}}$

answered Aug 31, 2011 at 19:32

22 votes

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Probability of winning a prize in a raffle

answered Dec 16, 2011 at 12:38

21 votes

Accepted

Weird measurable set

answered Dec 3, 2011 at 23:54

21 votes

Accepted

A fun Pascal-like triangle

answered Jul 27, 2011 at 5:48

20 votes

Accepted

Asymptotic behaviour of sums of consecutive powers

answered Sep 12, 2011 at 21:08

20 votes

Extending a function by continuity from a dense subset of a space

answered Oct 29, 2011 at 4:49

20 votes

Accepted

Find $ \lim\limits_{n\to\infty}\sum\limits_{i=1}^{n}{\frac{2n}{(n+2i)^2}} $

answered Oct 29, 2011 at 5:18

20 votes

Accepted

Proof that no permutation can be expressed both as the product of an even number of transpositions and as a product of an odd number of transpositions

answered Dec 27, 2011 at 2:50

20 votes

An algorithm for arbitrage in currency exchange

answered Dec 27, 2011 at 11:40

19 votes

Accepted

Does a median always exist for a random variable?

answered Nov 26, 2011 at 3:38

19 votes

Accepted

Show that $x^{35}+\dfrac{20205}{2+x^{17}+\cos^2x}=100$ has no root $x\in \mathbb{R}$

answered Oct 8, 2011 at 11:45

18 votes

Accepted

Proofs of $\lim\limits_{n \to \infty} \left(H_n - 2^{-n} \sum\limits_{k=1}^n \binom{n}{k} H_k\right) = \log 2$

answered Sep 11, 2011 at 4:53

18 votes

Motivation behind the definition of GCD and LCM

answered Nov 25, 2011 at 18:04

18 votes

How to find the equation of the tangent line to $y=x^2+2x-4$ at $x=2$?

answered Dec 17, 2011 at 4:01

18 votes

Is a norm a continuous function?

answered Jan 5, 2012 at 22:21

17 votes

Accepted

If $S$ and $T$ are nonempty subsets of a finite group $G$, then either $G=ST$ or $|G|\geq |S|+|T|$.

answered Jan 29, 2012 at 11:17

17 votes

Accepted

How do we show the equality of these two summations?

answered Nov 1, 2011 at 0:55

17 votes

Proofs of $\lim\limits_{n \to \infty} \left(H_n - 2^{-n} \sum\limits_{k=1}^n \binom{n}{k} H_k\right) = \log 2$

answered Sep 13, 2011 at 0:40

17 votes

What operations is a metric closed under?

answered Oct 3, 2011 at 3:42

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334 Answers

Check if a point is within an ellipse

A "fast" way for computing $ \prod \limits_{i=1}^{45}(1+\tan i^\circ) $?

Proving : $ \bigl(1+\frac{1}{n+1}\bigr)^{n+1} \gt (1+\frac{1}{n})^{n} $

What is your favorite application of the Pigeonhole Principle?

Integral: $\int_{-\infty}^{\infty} x^2 e^{-x^2}\mathrm dx$

What are the rules for equals signs with big-O and little-o?

Prove $\epsilon$-$\delta$ definition of continuity implies the open set definition for real function

Inequality involving $\limsup$ and $\liminf$: $ \liminf(a_{n+1}/a_n) \le \liminf a_n^{1/n} \le \limsup a_n^{1/n} \le \limsup(a_{n+1}/a_n)$

What is your favorite application of the Pigeonhole Principle?

Drunkard's walk on the $n^{th}$ roots of unity.

How does backwards induction work to prove a property for all naturals?

Nested Square Roots $5^0+\sqrt{5^1+\sqrt{5^2+\sqrt{5^4+\sqrt\dots}}}$

Probability of winning a prize in a raffle

Weird measurable set

A fun Pascal-like triangle

Asymptotic behaviour of sums of consecutive powers

Extending a function by continuity from a dense subset of a space

Find $ \lim\limits_{n\to\infty}\sum\limits_{i=1}^{n}{\frac{2n}{(n+2i)^2}} $

Proof that no permutation can be expressed both as the product of an even number of transpositions and as a product of an odd number of transpositions

An algorithm for arbitrage in currency exchange

Does a median always exist for a random variable?

Show that $x^{35}+\dfrac{20205}{2+x^{17}+\cos^2x}=100$ has no root $x\in \mathbb{R}$

Proofs of $\lim\limits_{n \to \infty} \left(H_n - 2^{-n} \sum\limits_{k=1}^n \binom{n}{k} H_k\right) = \log 2$

Motivation behind the definition of GCD and LCM

How to find the equation of the tangent line to $y=x^2+2x-4$ at $x=2$?

Is a norm a continuous function?

If $S$ and $T$ are nonempty subsets of a finite group $G$, then either $G=ST$ or $|G|\geq |S|+|T|$.

How do we show the equality of these two summations?

Proofs of $\lim\limits_{n \to \infty} \left(H_n - 2^{-n} \sum\limits_{k=1}^n \binom{n}{k} H_k\right) = \log 2$

What operations is a metric closed under?