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GinKin's user avatar
GinKin's user avatar
GinKin
  • Member for 10 years, 5 months
  • Last seen more than 9 years ago
21 votes
9 answers
2k views

Finding the limit of $\left(\frac{n}{n+1}\right)^n$

14 votes
3 answers
8k views

Proving $\limsup\frac 1 {a_n}=\frac 1 {\liminf a_n}$ and $\limsup a_n\cdot \limsup \frac 1 {a_n} \ge 1$

9 votes
3 answers
14k views

Prove that a given recursion sequence converges

8 votes
6 answers
5k views

Finding the limit $\displaystyle\lim_{x\to 0+} \left(\frac{\sin x}x\right)^{1/{x^2}}$ [duplicate]

8 votes
2 answers
525 views

Convergence of $\sum^\infty_{n=1}\frac{a_n}{1+n^2a_n}$

6 votes
3 answers
1k views

Proving $\frac2\pi x \le \sin x \le x$ for $x\in [0,\frac {\pi} 2]$

6 votes
5 answers
340 views

Showing a recursive sequence isn't bounded $a_{n+1}=a_n+\frac 1 {a_n}$

6 votes
2 answers
473 views

Convergence of $\sum_{k=1}^{\infty} \left (\sum_{j=1}^{k}\frac 1 j\right)^{-k}$

6 votes
3 answers
5k views

Radius of convergence and the endpoints of a power series

6 votes
2 answers
324 views

Proving $y=\lfloor x\rfloor$ doesn't have a primitive function

6 votes
3 answers
146 views

About the divergence of $\sum^\infty_{n=1}\frac 1 {n\cdot n^{1/n}}$

6 votes
5 answers
13k views

Showing $\sum^\infty_{n=1} \frac 1 {e^{\sqrt n}} $ converges

5 votes
4 answers
3k views

Convergence of $\sum^\infty_{n=1}\arctan(\frac 1 {\sqrt n}) $ and how to approach trigonometric expressions in sums

5 votes
3 answers
1k views

Let $f(x)$ be continuous on $[0,2]$, and differentiable on $(0,2)$ such that $0<f(1)<f(0)<f(2)$. Prove that $f'$ has a solution on $(0,2)$

5 votes
2 answers
688 views

Finding the basis of an intersection of subspaces

5 votes
5 answers
412 views

Finding: $\displaystyle\lim_{x\to\infty}x\big((1+\tfrac1x)^x-\mathrm{e}\big) $ [duplicate]

5 votes
1 answer
7k views

How to prove relation is asymmetric if it is both anti-symmetric and irreflexive

5 votes
4 answers
12k views

Proving $V$ is isomorphic to $W$ iff $\dim V=\dim W$

5 votes
1 answer
284 views

Proving for all polynomials $p(x)=p_0+p_1x+...+p_dx^d$, $ \ \sum^\infty_{n=1}p(a_n)$ converges iff $p_0=0$

5 votes
3 answers
475 views

A question about invertible matrices, $A,B$ are invertible matrices, $AB+BA=0$, show that n is even

4 votes
0 answers
283 views

Convergence of $\sum_{n=3}^{\infty}\frac{1}{n\log n(\log\log n)^\alpha} $

4 votes
1 answer
4k views

Uniform continuity of $\arctan x$

4 votes
2 answers
115 views

$f'$ is bounded and isn't continuous on $(a,b)$, so there's a point $y\in(a,b)$ such that $\lim_{x\to y}f'$ does not exist

4 votes
3 answers
215 views

Let $f$ be a differentiable function and for all $x$ $f'(x)>x$, prove $f$ isn't uniformly continuous

4 votes
1 answer
121 views

For what $\alpha$ does the series converge: $\sum^\infty_{n=2}\frac {1}{n^\alpha\log_2(n)}$

4 votes
1 answer
957 views

Cardinality of the set of all straight lines in $\mathbb R^2$

4 votes
1 answer
3k views

Is there always isomorphism between two sets that have the same cardinality?

4 votes
2 answers
10k views

Showing $a_n=\sin(n)$ does not converge [duplicate]

4 votes
4 answers
1k views

Is it true that $\det(A + I) = \operatorname{trace} (A) + 1$?

4 votes
3 answers
166 views

Proving $\cot x =\alpha x$ has a solution $\forall \alpha>0$ in $(0,\frac\pi2)$

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