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Riemann

I like math so much!

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33 Prove the following integral inequality: $\int_{0}^{1}f(g(x))dx\le\int_{0}^{1}f(x)dx+\int_{0}^{1}g(x)dx$ Jan 13 '13
16 Positive series problem: $\sum\limits_{n\geq1}a_n=+\infty$ implies $\sum_{n\geq1}\frac{a_n}{1+a_n}=+\infty$ Apr 14 '12
13 $f(f(x)f(y))+f(x+y)=f(xy)$ Jul 26 '17
13 Interesting limit: $I(n)=\lim_{x \to 0} (e^x-1)^{-n} - \left(\frac{x}{1!}+\frac {x^2}{2!}+\dotsb+\frac{x^n}{n!}\right)^{-n}$ Aug 26 '18
9 Does the sequence $(1,\frac{1}{2},\frac{1}{2^\frac{1}{2}},\frac{1}{3},\frac{1}{3^\frac{1}{2}},\frac{1}{3^\frac{1}{3}},\ldots)$ converge? Jan 20 '13
9 Recursive sequence - Convergency and Limit Apr 11 '12
9 Series problem! Can someone give me a counterexample? Apr 10 '12
7 Find limit $\lim_{n\to \infty}\frac{\sum_{k=1}^n k^n}{n^n}$. Jul 31 '18
7 Monotonicity of the function $(1+x)^{\frac{1}{x}}\left(1+\frac{1}{x}\right)^x$. Sep 7 '18
7 Finding limit from Squeeze theorem: $\lim\limits_{n\to\infty} \left(\frac{2n-5}{3n+1}\right)^n$ Aug 26 '18
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