# Amihai Zivan

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# 37 Questions

 30 Why is $\int_{0}^{\infty} \frac {\ln x}{1+x^2} \mathrm{d}x =0$? 26 Interesting Math for 3-graders 11 Construction of a right triangle 11 What's the name of this quantity? 7 dissection of a $1\times 5$ rectangle to a square

# 1,568 Reputation

 +15 Proving that $\int_0 ^1 \frac{\text{d}s}{\sqrt{1-s^2}}$ converges with no trig functions -3 Proving $\int x \, \mathrm{d}y =xy- \int y \, \mathrm{d}x$ +15 Is it a “paradox”, or a flaw in the question? +5 Why is $\int_{0}^{\infty} \frac {\ln x}{1+x^2} \mathrm{d}x =0$?

 16 What is a good book to study linear algebra? 6 Prove that $n! > \sqrt{n^n}, n \geq 3$ 4 What is the limit value of $a$ that $\sum\limits_{k = 1 }^ \infty \frac{ \ln(k)}{k^a}$ converges 3 Prove the sum $\sum_{n=1}^\infty \frac{\arctan{n}}{n}$ diverges. 3 Show that $\displaystyle \lim_{n \rightarrow \infty} \sqrt[n]{a} =1$

# 53 Tags

 19 sequences-and-series × 16 5 real-analysis × 7 11 calculus × 25 5 convergence × 3 11 limits × 10 5 exponentiation × 2 7 linear-algebra × 5 3 matrices × 3 6 number-theory 3 algorithms × 2

# 6 Accounts

 Mathematics 1,568 rep 721 TeX - LaTeX 130 rep 4 Stack Overflow 103 rep 2 Theoretical Computer Science 101 rep 1 Mi Yodeya 101 rep