Mathematics
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All Questions Answers
Score Newest
question
16
Show that there are no real solutions of $1 + \sum_{n = 1}^{\infty} \frac{x^n}{\prod_{k=1}^{n} H_k} = 0$ where $H_k = \sum_{i=1}^{k} \frac{1}{i}.$
Aug 9, 2021
question
12
Combinatorial proof of $\sum_{k=0}^{n} k \binom{n+1}{k+1} n^{n-k} = n^{n+1}$
Apr 11
question
11
Find all positive integers s.t. $\frac{1}{a^2} - \frac{1}{b^2} = \frac{1}{c^2} - \frac{1}{d^2}$
Jan 31
question
8
For $1 \not= \alpha \in \mathbb{C}$ such that $\alpha^7 = 1$, evaluate $\alpha + \alpha^2 + \alpha^4.$
Aug 10, 2021
question
8
Evaluate $\prod_{p \in \mathbb{P}} \left( 1 + \frac{3p^2}{(p^2 - 1)^2} \right)$ for prime numbers $p$, where $p = 14k \pm 1$ or $p = 18k \pm 1$
Aug 29, 2021
question
3
Evaluate the following : $\lim_{n \to \infty} \left\{ \frac{n!}{\prod_{k=1}^{n} H_k} \right\}^{\frac{1}{n}}$ where $H_k = \sum_{i=1}^{k} \frac{1}{i}$.
Aug 31, 2021
question
3
Find function $f$ such that $f(1) = 1$ and $f'(x) = \frac{1}{x^2 + \left\{ f(x) \right\}^2}.$
Aug 10, 2021
answer
3
Calculating $\int_0^\infty \frac{1}{(x^2+1)^n}dx$
Aug 12, 2021
question
2
True or False : What are some tricky questions in calculus? (or in overall) [closed]
Aug 11, 2021
question
2
Easier proof of : Show that for all $n \in \mathbb{Z}$, there exists $a, b, c \in \mathbb{Z}$ such that $n = a^2 + b^2 - c^3.$ [duplicate]
Aug 9, 2021

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