# GinKin

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# 165 Questions

 21 Finding the limit of $\left(\frac{n}{n+1}\right)^n$ 6 Convergence of $\sum_{k=1}^{\infty} \left (\sum_{j=1}^{k}\frac 1 j\right)^{-k}$ 6 Finding the limit $\displaystyle\lim_{x\to 0+} \left(\frac{\sin x}x\right)^{1/{x^2}}$ 5 Proving $\limsup\frac 1 {a_n}=\frac 1 {\liminf a_n}$ and $\limsup a_n\cdot \limsup \frac 1 {a_n} \ge 1$ 5 Radius of convergence and the endpoints of a power series

# 1,618 Reputation

 -2 Why is $\lim\limits_{n \to \infty} \frac{1}{n} \sqrt[n] {n^n}=1$ where $\lim\limits_{n \to \infty} \sqrt[n] {n!}=\infty$? +5 How can I learn to write proofs more formally or rigourusly? +5 Proving $\limsup\frac 1 {a_n}=\frac 1 {\liminf a_n}$ and $\limsup a_n\cdot \limsup \frac 1 {a_n} \ge 1$ +5 $\exists x_0$ such that $f(f(x_0))=x_0$ prove that $f$ has a fixed point

 3 Beautiful Mathematical Images 1 Finding a three digit number, with properties of a geometric progression such that by subtracting 400 forms an arithmetic progression number 1 Prove $x^{2 \over 3} \ln(x)$ is uniformly continious 1 Finding a matrix that satisfy the following row and column requirements 0 How can we prove these equivalence relations

# 48 Tags

 1 linear-algebra × 37 1 real-analysis × 9 1 sequences-and-series × 31 1 continuity × 8 1 limits × 21 1 solution-verification × 6 1 matrices × 10 0 calculus × 90 1 functions × 10 0 elementary-set-theory × 30

# 7 Accounts

 Mathematics 1,618 rep 423 Stack Overflow 139 rep 5 Skeptics 126 rep 6 English Language & Usage 120 rep 4 Super User 106 rep 3