# Chon

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# 83 Questions

 26 Computing $\sum\limits_{i=1}^{\infty}\sum\limits_{j=1}^{\infty} \frac{(-1)^{i+j}}{i+j}$ 25 Proving $\int_{0}^{\infty} \frac{\ln(t)}{\sqrt{t}}e^{-t} \mathrm dt=-\sqrt{\pi}(\gamma+\ln{4})$ 24 Computing $\zeta(6)=\sum\limits_{k=1}^\infty \frac1{k^6}$ with Fourier series. 16 On computing: $\gcd \left({2n \choose 1}, {2n \choose 3},\cdots, {2n \choose 2n-1}\right)$ 15 Proving that $2$ is the only real solution of $3^x+4^x=5^x$

# 2,517 Reputation

 +5 Computing $\sum\limits_{i=1}^{\infty}\sum\limits_{j=1}^{\infty} \frac{(-1)^{i+j}}{i+j}$ +5 Proving that $2$ is the only real solution of $3^x+4^x=5^x$ +5 Computing $\zeta(6)=\sum\limits_{k=1}^\infty \frac1{k^6}$ with Fourier series. +10 A proof of $\int_{0}^{1}\left( \frac{\ln t}{1-t}\right)^2\,\mathrm{d}t=\frac{\pi^2}{3}$

 9 Computing $\sum_{n=1}^{\infty} \frac{\lfloor{\sqrt{n+1}}\rfloor-\lfloor{\sqrt{n}}\rfloor}{n}$ 6 A proof of $\int_{0}^{1}\left( \frac{\ln t}{1-t}\right)^2\,\mathrm{d}t=\frac{\pi^2}{3}$ 3 Finding the exact value of $\sum \frac{4n-3}{n(n^2-4)}$ 1 Nature of the series $\sum u_{n}, u_{n}=n!\prod_{k=1}^n \sin\left(\frac{x}{k}\right)$ 1 Computing $\int_{0}^{2\pi}\frac{\sin(nx)}{\sin(x)} \mathrm dx$

# 28 Tags

 18 real-analysis × 24 6 definite-integrals × 3 13 sequences-and-series × 42 1 analysis × 7 7 integration × 22 0 asymptotics × 14 6 calculus × 10 0 trigonometry × 6 6 improper-integrals × 4 0 inequality × 6

# 1 Account

 Mathematics 2,517 rep 724