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John Chessant

San Francisco, CA

BY DAY: I am a student. BY NIGHT: I am a student.

I like maths and science!!!

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Top Questions
16 votes

Prove: $\lim_{n\to\infty}{\sum_{m=0}^{n}{\sum_{k=0}^{n-m}{\frac{2^{n-m-k}}{n-m+1}\,\frac{{{2k}\choose{k}}{{2m}\choose{m}}}{{{2n}\choose{n}}}}}}=\pi$

limits proof-verification summation binomial-coefficients alternative-proof asked Dec 31, 2018 at 18:54
math.stackexchange.com

13 votes

Evaluate $\int_{0}^{\pi/2}{\frac{d\theta}{{\left(\cos^3{\theta}+\sin^3{\theta}\right)}^{2/3}}}$

integration definite-integrals trigonometric-integrals asked Aug 2, 2017 at 14:59
math.stackexchange.com

10 votes

Interesting Array of Integers with Strange Pattern

matrices arithmetic asked Jun 3, 2015 at 1:14
math.stackexchange.com

8 votes

Random Sequence of Alternating Increase/Decrease Numbers

integration combinatorics permutations expectation random asked Jun 10, 2015 at 19:03
math.stackexchange.com

8 votes

Evaluate $\sum_{n=1}^{\infty} {\left(\frac{(-1)^n}{n}\sum_{k=1}^n {\left(\frac{(-1)^k}{k}\right)}\right)}$

summation asked Jun 14, 2017 at 0:50
math.stackexchange.com

8 votes

Calculate $\tan^2{\frac{\pi}{5}}+\tan^2{\frac{2\pi}{5}}$ without a calculator

algebra-precalculus trigonometry polynomials roots fractions asked Jun 25, 2017 at 22:51
math.stackexchange.com

8 votes

Prove: $\int_{0}^{\pi/2}{\sqrt{1 + \sqrt{1 + (\tan{x})^{2/3}}}\,dx} = \frac{\pi}{2} (3^{1/4} + 3^{3/4} - 2)$

calculus integration definite-integrals improper-integrals asked Jun 19, 2020 at 21:36
math.stackexchange.com

6 votes

Evaluate $\int_0^\pi\frac{\ln\left(1+\cos\theta\right)}{\cos\theta}\,d\theta$

integration definite-integrals asked Aug 8, 2017 at 20:15
math.stackexchange.com

6 votes

Compute $\sum\limits_{n=1}^\infty\frac{b_{n-1}}{n 2^n}$ where $b_n=\sum\limits_{k=0}^n\frac{2^k}{k+1}$

sequences-and-series summation asked May 26, 2017 at 1:03
math.stackexchange.com

5 votes

Add 4 to each digit and multiply

arithmetic contest-math asked Aug 1, 2017 at 11:33
math.stackexchange.com

1 2

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