User Amihai Zivan - Mathematics Stack Exchange

49 votes

Accepted

What is a good book to study linear algebra?

answered Jun 18, 2012 at 21:14

10 votes

Calculating the limit $\lim((n!)^{1/n})$

answered Mar 10, 2014 at 8:37

7 votes

Prove that $n! > \sqrt{n^n}, n \geq 3$

answered Feb 5, 2012 at 22:47

6 votes

Show that $A_n=\sum\limits_{k=1}^n \sin k $ is bounded?

answered May 23, 2012 at 17:37

6 votes

Accepted

Show that $\lim_{n \rightarrow \infty} \sqrt[n]{a} =1$

answered Feb 17, 2014 at 9:59

4 votes

Limit of f(x) knowing limit of f(x)/x

answered Apr 13, 2015 at 12:39

4 votes

Show that this limit is equal to $\liminf a_{n}^{1/n}$ for positive terms.

answered Jun 4, 2012 at 19:48

4 votes

Accepted

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

answered Jun 12, 2012 at 7:12

4 votes

Accepted

What is the limit value of $a$ that $\sum\limits_{k = 1 }^ \infty \frac{ \ln(k)}{k^a}$ converges

answered Jul 25, 2012 at 10:23

4 votes

Accepted

Approximating Increasing Sequence

answered Dec 31, 2012 at 9:38

3 votes

Proving that the matrix is not invertible.

answered Nov 23, 2012 at 12:19

3 votes

Where do I start with self learning linear algebra

answered May 16, 2012 at 19:41

3 votes

Prove the sum $\sum_{n=1}^\infty \frac{\arctan{n}}{n}$ diverges.

answered Jun 9, 2014 at 12:20

3 votes

Let $A,B$ be $n \times n$ matrices so that $AB = 0$ If $A,B \neq 0$ what do I know about $A$ and $B$?

answered Jun 1, 2013 at 21:27

2 votes

Does $\sum_{n=1}^{\infty} \frac{1}{n+1}$ converge?

answered Jul 9, 2013 at 11:37

2 votes

Accepted

pow$(X,Y)$ $>$ pow$(Y,X)$, if $X<Y$.

answered Jan 1, 2013 at 7:23

2 votes

Limit with parameter, $(e^{-1/x^2})/x^a$

answered Jan 11, 2013 at 6:07

2 votes

If $ \displaystyle F(x) = \int_{1}^{3 x} \frac{1}{t} ~ \mathrm{d}{t} $, find $ F'(x) $.

answered Nov 21, 2012 at 5:07

2 votes

Limit of square root without L'Hopital's rule.

answered Oct 28, 2012 at 20:26

1 vote

How to show that $\lim_{n \rightarrow \infty} (\frac{n}{n+a})^n = \frac{1}{e^a}$?

answered Oct 30, 2012 at 14:06

1 vote

Integral as a limit of a sum

answered Jun 22, 2012 at 15:12

1 vote

A Taylor Expansion Problem

answered Dec 20, 2012 at 21:00

1 vote

find the limit as $n \rightarrow \infty$ of $\frac{\sin(n)-n}{n^3}$

answered Apr 29, 2012 at 18:07

1 vote

How do I show that $T$ is invertible?

answered Mar 13, 2013 at 13:32

1 vote

Accepted

Does there exist a sequence such that $\lim\limits_{n\to\infty}\frac{n(a_{n+1}-a_{n})+1}{a_{n}}=0$?

answered Nov 25, 2013 at 9:59

0 votes

Prove that $\sqrt[n]{n!}$ is increasing and diverges

answered Nov 25, 2013 at 11:41

0 votes

Does $\sum_{n=1}^{\infty} \frac{\ln(n)}{n^2+2}$ converge?

answered Jun 23, 2013 at 7:03

0 votes

For what real number $r$ does the series $\sum_{n=1}^{\infty}\frac{\ln(n)}{n^r}$ converge?

answered Apr 17, 2013 at 6:50

0 votes

How to differentiate $f(x) = 1-xe^{1-x}$ w.r.t. $x$?

answered Apr 8, 2014 at 19:38

0 votes

What is limit of $e^{x}/\ln(x)$ as $x \rightarrow +\infty$

answered Apr 12, 2014 at 17:58

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37 Answers

What is a good book to study linear algebra?

Calculating the limit $\lim((n!)^{1/n})$

Prove that $n! > \sqrt{n^n}, n \geq 3$

Show that $A_n=\sum\limits_{k=1}^n \sin k $ is bounded?

Show that $\lim_{n \rightarrow \infty} \sqrt[n]{a} =1$

Limit of f(x) knowing limit of f(x)/x

Show that this limit is equal to $\liminf a_{n}^{1/n}$ for positive terms.

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

What is the limit value of $a$ that $\sum\limits_{k = 1 }^ \infty \frac{ \ln(k)}{k^a}$ converges

Approximating Increasing Sequence

Proving that the matrix is not invertible.

Where do I start with self learning linear algebra

Prove the sum $\sum_{n=1}^\infty \frac{\arctan{n}}{n}$ diverges.

Let $A,B$ be $n \times n$ matrices so that $AB = 0$ If $A,B \neq 0$ what do I know about $A$ and $B$?

Does $\sum_{n=1}^{\infty} \frac{1}{n+1}$ converge?

pow$(X,Y)$ $>$ pow$(Y,X)$, if $X<Y$.

Limit with parameter, $(e^{-1/x^2})/x^a$

If $ \displaystyle F(x) = \int_{1}^{3 x} \frac{1}{t} ~ \mathrm{d}{t} $, find $ F'(x) $.

Limit of square root without L'Hopital's rule.

How to show that $\lim_{n \rightarrow \infty} (\frac{n}{n+a})^n = \frac{1}{e^a}$?

Integral as a limit of a sum

A Taylor Expansion Problem

find the limit as $n \rightarrow \infty$ of $\frac{\sin(n)-n}{n^3}$

How do I show that $T$ is invertible?

Does there exist a sequence such that $\lim\limits_{n\to\infty}\frac{n(a_{n+1}-a_{n})+1}{a_{n}}=0$?

Prove that $\sqrt[n]{n!}$ is increasing and diverges

Does $\sum_{n=1}^{\infty} \frac{\ln(n)}{n^2+2}$ converge?

For what real number $r$ does the series $\sum_{n=1}^{\infty}\frac{\ln(n)}{n^r}$ converge?

How to differentiate $f(x) = 1-xe^{1-x}$ w.r.t. $x$?

What is limit of $e^{x}/\ln(x)$ as $x \rightarrow +\infty$