Mathematics
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Ant
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question
16
Prove: $\lim_{n\to\infty}{\sum_{m=0}^{n}{\sum_{k=0}^{n-m}{\frac{2^{n-m-k}}{n-m+1}\,\frac{{{2k}\choose{k}}{{2m}\choose{m}}}{{{2n}\choose{n}}}}}}=\pi$
Dec 31, 2018
answer
16
Solving the integral $\int x\sqrt{1+x}\ dx $
Jun 16, 2015
question
13
Evaluate $\int_{0}^{\pi/2}{\frac{d\theta}{{\left(\cos^3{\theta}+\sin^3{\theta}\right)}^{2/3}}}$
Aug 2, 2017
answer
12
Is $15/52$ equal to $17/59$?
May 21, 2015
answer
9
Fibonacci Identity with Binomial Coefficients
Nov 6, 2016
answer
9
Rolling two dice, what is the probability that two consecutive $7$s happens earlier than a $12$?
May 27, 2015
question
8
Evaluate $\sum_{n=1}^{\infty} {\left(\frac{(-1)^n}{n}\sum_{k=1}^n {\left(\frac{(-1)^k}{k}\right)}\right)}$
Jun 14, 2017
question
8
Calculate $\tan^2{\frac{\pi}{5}}+\tan^2{\frac{2\pi}{5}}$ without a calculator
Jun 25, 2017
question
8
Prove: $\int_{0}^{\pi/2}{\sqrt{1 + \sqrt{1 + (\tan{x})^{2/3}}}\,dx} = \frac{\pi}{2} (3^{1/4} + 3^{3/4} - 2)$
Jun 19, 2020
question
6
Compute $\sum\limits_{n=1}^\infty\frac{b_{n-1}}{n 2^n}$ where $b_n=\sum\limits_{k=0}^n\frac{2^k}{k+1}$
May 26, 2017

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