### Questions (113)

 16 $e^{\left(\pi^{(e^\pi)}\right)}\;$ or $\;\pi^{\left(e^{(\pi^e)}\right)}$. Which one is greater than the other? 10 Calculate $\int_{-\infty}^{+\infty}\frac{x}{1+x^2}dx$, what is wrong with this? 9 Problem with calculation this integral: $\int_0^\pi \frac{dx}{1+3\sin^2x}$ 9 Is this inequality provable? $e^{\left(\pi^{e^{\pi^{.^{.^{.^{e^\pi}}}}}}\right)}\ge \pi^{\left(e^{\pi^{e^{.^{.^{.^{\pi^e}}}}}}\right)}$ 7 Calculating the series $1/8+1/88+1/888+…$

### Reputation (2,170)

 +10 $\sum_{k=0}^n\binom{n}{k}(-1)^k(k+1)$ Am I true? +20 $A=\{a_{\lambda_1}+a_{\lambda_2}+…+a_{\lambda_k}| k\in\mathbb N, \lambda_1,…,\lambda_k\in\mathbb R \;\text{are all distinct}\}$ is not bounded +10 What is the elementary methods?How we define elementary methods for integrals?And why we just can't solve these with elementary methods? +10 Problem with calculation this integral: $\int_0^\pi \frac{dx}{1+3\sin^2x}$

### Answers (13)

 4 $\lim_{n\to \infty} \sum_{i=0}^n \frac {r^i}{i!} = e^r$ 2 Given $y_n=(1+\frac{1}{n})^{n+1}$ show that $\lbrace y_n \rbrace$ is a decreasing sequence 1 Are there any Symmetric Groups that are cyclic? 1 Is there a simple proof for the irrationality or transcendence of $e^{q}$ where $q \in \mathbb{Q}$? 1 How to write the formula in Disjunctive Normal Form (DNF)?

### Tags (85)

 6 sequences-and-series × 16 1 group-theory × 10 4 calculus × 15 1 abstract-algebra × 7 4 limits × 10 1 analysis × 4 4 summation × 2 1 permutations × 4 2 real-analysis × 21 1 algebra-precalculus × 3

### Bookmarks (154)

 321 How can you prove that a function has no closed form integral? 299 Nice examples of groups which are not obviously groups 265 Really advanced techniques of integration (definite or indefinite) 254 What is the maximum volume that can be contained by a sheet of paper? 182 When can you switch the order of limits?

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