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Jack Tiger Lam's user avatar
Jack Tiger Lam's user avatar
Jack Tiger Lam's user avatar
Jack Tiger Lam
  • Member for 9 years, 7 months
  • Last seen more than a week ago
33 votes
1 answer
473 views

Closure of $\left\{\frac{\tan{n}}{n} | \, n \in \mathbb{N}\right\}$

31 votes
3 answers
1k views

Bizarre Definite Integral

18 votes
1 answer
410 views

Combinatorial Geometric proof of $\binom{\binom{n}{2}}{3} > \binom{\binom{n}{3}}{2}$

10 votes
1 answer
241 views

Combinatorial Proof for $\sum_{k=0}^n \binom{2n}{2k}^2 = \frac{1}{2}\left( \binom{4n}{2n}+(-1)^n \binom{2n}{n} \right)$

10 votes
0 answers
449 views

Divisibility of term in exponential recurrence relation

8 votes
1 answer
495 views

Integral $\small \int_0^\infty \frac{(\pi x - 2\log{x})^3}{\left(\log^2{x} + \frac{\pi^2}{4}\right)(1+x^2)^2} \text{d}x$

7 votes
0 answers
337 views

Existence of a factorisation proof of the AM-GM inequality [closed]

7 votes
2 answers
309 views

Gamma-Distribution-like integral

6 votes
0 answers
788 views

Weird use of Glasser's Master Theorem

6 votes
0 answers
159 views

Solution to an equation involving continued fractions and decimal expansion.

6 votes
1 answer
260 views

Ab*surd* Integrals

6 votes
1 answer
205 views

Finite Messy Trigonometric Sum

5 votes
2 answers
301 views

Solving $ a(n+1) = a(n) + \frac{1}{a(n)}$ with $a(1) = 1 $

5 votes
1 answer
269 views

Proof of Binomial Sum via Double Counting

5 votes
1 answer
436 views

Infinite Triple Sum

5 votes
2 answers
140 views

How to prove that $\frac{1}{2} \left( 1 - \sqrt{3} \pm i \sqrt{2} \sqrt[4]{3} \right)$ is not a root of unity?

5 votes
1 answer
162 views

Evaluating trivial integral with linear algebra

5 votes
3 answers
128 views

Strengthening the Log-Concavity of Binomial Coefficients: $\binom{n}{k-1}\binom{n}{k+1} < \binom{n}{k}^2 - \binom{n}{k}$

4 votes
1 answer
86 views

How to prove $\int_0^\frac{\pi}{2} \sin^{r} \theta d \theta \int_0^\frac{\pi}{2} \sin^{r-1} \theta d \theta = \frac{\pi}{2r}$ without Beta properties?

4 votes
1 answer
109 views

Combinatorial proof of $\binom{n^2}{2} = 2\left(\binom{\binom{n+1}{2}}{2}+\binom{\binom{n}{2}}{2}\right)$

4 votes
2 answers
88 views

Non-trivial gap in a field extension problem proof

4 votes
1 answer
81 views

Proving Zeta Relations Without Direct Evaluation

4 votes
1 answer
926 views

Lower bound for roots of a polynomial with positive coefficients.

4 votes
3 answers
349 views

Prove $\int_0^1 \frac{x-1}{(x+1)\log{x}} \text{d}x = \log{\frac{\pi}{2}}$

3 votes
3 answers
3k views

How did the Ancient Greeks know that the circle method of finding square roots was mathematically valid? How do we know that?

3 votes
1 answer
2k views

Looking for an alternative proof of the angle difference expansion

3 votes
2 answers
386 views

Probability of a painted cube being reassembled into itself

3 votes
2 answers
317 views

Inequality of convex plus concave function

3 votes
2 answers
182 views

Prove $\int_0^2 \frac{\log{x}}{\sqrt{4-x^2}}\text{d}x=0$ without integrating

2 votes
3 answers
105 views

Nice way of showing the locus of $\left|z-\frac{1}{z}\right| = 2$ is the union of 2 intersecting circles.