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 7 Prove $\sin x$ is uniformly continuous on $\mathbb R$ 3 Limit for a Recurrence Relation 3 How to prove $\sum_{n=1}^{\infty}\left|\frac{a_{1}+\cdots+a_{n}}{n}\right|^{p}\leq\left(\frac{p}{p-1}\right)^{p}\sum_{n=1}^{\infty}|a_{n}|^{p}$ 3 How to show $\sum_{n=j}^{\infty}n^{-\alpha/p}\leq j^{-\alpha/p}+\frac{p}{\alpha-p}j^{(p-\alpha)/p}$ 3 little-o and its properties

# 947 Reputation

 +2 Show that $\left| \mathbb{P}(X=m)-\mathbb{P}(Y=m) \right| \le \mathbb{P}(Y\ne X)$ +2 Does $\theta(n)$ = $1/x$ make any sense? +10 Prove $\sin x$ is uniformly continuous on $\mathbb R$ +2 How to prove the eigenvalues of tridiagonal matrix?

# 19 Questions

 8 Convergence of $\int\limits_{\mathbb{R}}\sum\limits_{n=1}^\infty f(nx+n!)dx$ 7 Sources on Several Complex Variables 6 How to apply Borel-Cantelli Lemma? 5 Convergence of $\int\int_{|x|\geq 1,|y|\geq 1} \frac{1}{|x|^\alpha+ |y|^\beta} \;dx\;dy$ 4 Domain of Holomorphy

# 40 Tags

 12 calculus × 7 6 inequality × 3 8 real-analysis × 10 6 limits × 2 7 continuity 5 differential-equations × 5 7 functions 4 analysis × 2 6 asymptotics × 6 3 sequences-and-series × 3

# 5 Accounts

 Mathematics 947 rep 517 History 245 rep 16 Philosophy 101 rep 1 Russian Language 101 rep MathOverflow 101 rep 2