### Answers (157)

 17 How do I prove that an anti-symmetric matrix $A$ is not invertible? 16 Evaluating limit by sandwich theorem: $\lim_{n\to\ \infty}\frac{1}{1+n^2} +\frac{2}{2+n^2}+\cdots+\frac{n}{n+n^2}$ 10 What are some counter-intuitive results in mathematics that involve only finite objects? 10 Mathematicians who overcame academic failure to achieve success 9 For matrices $A, B$, show that $BA = 0 \Rightarrow (AB)^2 = 0$

### Reputation (5,120)

 +5 Let ${f_n}$ be a sequence of continuous real valued functions on $[0, \infty)$, then which of the following is/are true? +5 Find the solution of the Cauchy problem $u_t-uu_x=0$. +5 Existence of a holomorphic function in the open disc $D=\{z\in \mathbb{C}: |z|<1\}$. +5 Let $A$ be an $n\times n$ matrices over $\mathbb{C}$ then which of the following are true?

### Questions (134)

 22 What is the limit of $\frac{1}{\sqrt{n}}\sum_{k=1}^n\frac{1}{\sqrt{2k-1}+\sqrt{2k+1}}$? 10 Find the limit of $\frac{(n+1)^\sqrt{n+1}}{n^\sqrt{n}}$. 10 What are some of the best book in mathematics for general reader? [closed] 8 Existence of an $n\times n$ real matrix $A$ such that $A^2=-I$. 6 How many ways can we define prime number?

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