User Dominic Michaelis - Mathematics Stack Exchange

38 votes

Accepted

Critiques on proof showing $\sqrt{12}$ is irrational.

answered Feb 16, 2013 at 15:21

28 votes

How to prove $\det \left(e^A\right) = e^{\operatorname{tr}(A)}$?

answered Mar 6, 2013 at 15:26

28 votes

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Find $\lim_{n \to \infty}\frac{\sin 1+2\sin \frac{1}{2}+\cdots+n\sin \frac{1}{n}}{n}$

answered May 13, 2013 at 5:37

25 votes

Could I be using proof by contradiction too much?

answered Mar 3, 2013 at 22:35

24 votes

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Why can the intersection of infinite open sets be closed?

answered Mar 24, 2013 at 19:07

22 votes

How do I show that a matrix is injective?

answered Mar 3, 2013 at 18:30

21 votes

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Difference between the Laurent and Taylor Series.

answered Apr 13, 2013 at 8:51

19 votes

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How to determine the exact value of $\sin(585^\circ)$?

answered Apr 7, 2013 at 11:08

16 votes

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Is there a short proof for the Intermediate Value Theorem

answered Apr 10, 2013 at 11:55

16 votes

The series $\sum_{n=1}^{+\infty}\frac{1}{1^2+2^2+\cdots+n^2}.$

answered Feb 28, 2013 at 21:30

14 votes

A symmetric matrix whose square is zero

answered Apr 11, 2013 at 16:30

14 votes

Why is it important to have a discrepancy between image and codomain?

answered May 19, 2013 at 16:19

13 votes

Difference between $\mathbb C$ and $\mathbb R^2$

answered Apr 17, 2013 at 4:21

13 votes

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Radius of convergence of a sum of power series

answered Feb 20, 2013 at 20:26

13 votes

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Does a function exist with the property $f(-n^2+3n+1)=(f(n))^2+1$?

answered Mar 26, 2013 at 7:25

12 votes

Prove $3|n(n+1)(n+2)$ by induction

answered Sep 18, 2013 at 20:12

11 votes

how to prove that$\sum_{n=1}^{\infty}{ n^4\over n!}=15e$

answered Aug 29, 2013 at 11:50

11 votes

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Example of a set $Y$ that has zero Lebesgue measure and a continuous function $f$ such that $f(Y)$ is not a set of zero Lebesgue measure.

answered Aug 29, 2013 at 17:18

11 votes

Examples of non-cyclic group with a cyclic automorphism group

answered May 22, 2013 at 20:08

11 votes

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What is the property that allows $5^{2x+1} = 5^2$ to become $2x+1 = 2$?

answered Mar 20, 2013 at 18:55

10 votes

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How to prove that $\lim\limits_{n\to\infty} \frac{n!}{n^2}$ diverges to infinity?

answered Mar 8, 2013 at 9:23

10 votes

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If $f$ is analytic where $f$ is represented as $f=g.h$ where $g$ is analytic . From here can we conclude that $h$ is analytic?

answered Mar 17, 2013 at 15:35

10 votes

Diagonalizable upper triangular matrices

answered Feb 18, 2013 at 17:00

10 votes

Where are the values of the sine function coming from?

answered Feb 17, 2013 at 17:01

10 votes

$xy=1 \implies $minimum $x+y=$?

answered Mar 1, 2013 at 13:16

10 votes

Determinant of matrix exponential?

answered Mar 1, 2013 at 20:39

9 votes

Accepted

composition of continuous functions

answered Mar 2, 2013 at 13:08

9 votes

Accepted

How to evaluate $\sum\limits_{n=1}^{+\infty}\frac{1}{1^k+2^k+\cdots+n^k}$?

answered Feb 28, 2013 at 23:47

8 votes

Find the value $\sum_{n=1}^{\infty}(e-(1+\frac{1}{n})^n)$

answered Mar 3, 2013 at 23:10

8 votes

If $\sum_{n}A_n$ is convergent, then $\sum_{n} (-1)^{n} A_n$ is also convergent?

answered Feb 16, 2013 at 10:24

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507 Answers

Critiques on proof showing $\sqrt{12}$ is irrational.

How to prove $\det \left(e^A\right) = e^{\operatorname{tr}(A)}$?

Find $\lim_{n \to \infty}\frac{\sin 1+2\sin \frac{1}{2}+\cdots+n\sin \frac{1}{n}}{n}$

Could I be using proof by contradiction too much?

Why can the intersection of infinite open sets be closed?

How do I show that a matrix is injective?

Difference between the Laurent and Taylor Series.

How to determine the exact value of $\sin(585^\circ)$?

Is there a short proof for the Intermediate Value Theorem

The series $\sum_{n=1}^{+\infty}\frac{1}{1^2+2^2+\cdots+n^2}.$

A symmetric matrix whose square is zero

Why is it important to have a discrepancy between image and codomain?

Difference between $\mathbb C$ and $\mathbb R^2$

Radius of convergence of a sum of power series

Does a function exist with the property $f(-n^2+3n+1)=(f(n))^2+1$?

Prove $3|n(n+1)(n+2)$ by induction

how to prove that$\sum_{n=1}^{\infty}{ n^4\over n!}=15e$

Example of a set $Y$ that has zero Lebesgue measure and a continuous function $f$ such that $f(Y)$ is not a set of zero Lebesgue measure.

Examples of non-cyclic group with a cyclic automorphism group

What is the property that allows $5^{2x+1} = 5^2$ to become $2x+1 = 2$?

How to prove that $\lim\limits_{n\to\infty} \frac{n!}{n^2}$ diverges to infinity?

If $f$ is analytic where $f$ is represented as $f=g.h$ where $g$ is analytic . From here can we conclude that $h$ is analytic?

Diagonalizable upper triangular matrices

Where are the values of the sine function coming from?

$xy=1 \implies $minimum $x+y=$?

Determinant of matrix exponential?

composition of continuous functions

How to evaluate $\sum\limits_{n=1}^{+\infty}\frac{1}{1^k+2^k+\cdots+n^k}$?

Find the value $\sum_{n=1}^{\infty}(e-(1+\frac{1}{n})^n)$

If $\sum_{n}A_n$ is convergent, then $\sum_{n} (-1)^{n} A_n$ is also convergent?