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trancelocation
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40 votes

How to prove that if the determinant of the matrix is zero then at least one eigenvalue must be zero?

14 votes

Determinant of a matrix and linear independence (explanation needed)

14 votes

Why does Wolfram|Alpha make a mistake here?

14 votes
Accepted

Converting an infinite series to a definite integral

12 votes
Accepted

Integration by Parts only of $\sqrt{1-u^2}$

12 votes

Any rectangular shape on a calculator numpad when divided by 11 gives an integer. Why?

12 votes
Accepted

How to solve $\lim _{x\to \infty}\dfrac{x^5}{2^x} $ without L'Hospital's Rule

11 votes

Completing the square to solve limit problems

11 votes

Four married couples attend a party. Each person shakes hands with every other person, except their own spouse, exactly once. How many handshakes?

11 votes
Accepted

A strange trigonometric identity

10 votes

Is it alright to substitute $0$ for $1/n$ in this limit problem?

10 votes
Accepted

Integrate $\frac{1}{x\,\log{x}}$ by parts

9 votes

Proof by induction with square root in denominator: $\frac1{2\sqrt1}+\frac1{3\sqrt2}+\dots+ \frac1{(n+1)\sqrt n} < 2-\frac2{\sqrt{(n+1)}}$

9 votes
Accepted

prove existence of the limit of a sequence

9 votes
Accepted

How to prove that $ a^2+b^2+c^2=1$ implies $ab+bc+ca \in [-\frac12,1]$?

9 votes

Every convergent sequence is bounded: what's wrong with this counterexample?

9 votes
Accepted

Drawing without replacement: why is the order of draw irrelevant?

9 votes

Prove that the minimum values of $x^2+y^2+z^2$ is $27$ with given condition $\dfrac{1}{x}+\dfrac{1}{y}+\dfrac{1}{z}=1$.

9 votes
Accepted

Why is $\frac{1}{\sqrt 5}\left[\left(\frac{1+\sqrt 5}{2}\right)^n-\left(\frac{1-\sqrt 5}{2}\right)^n\right]$ an integer?

9 votes
Accepted

verifying $\lim\limits_{x \to \infty} (1+\frac{1}{\sqrt{x}})^x$

9 votes
Accepted

How to prove that $\lim\limits_{n \to \infty} \frac{(n!)^n}{n^{n^2}}=0$?

8 votes
Accepted

An interesting problem of polynomials

8 votes

Proof by induction:$\frac{3}{5}\cdot\frac{7}{9}\cdot\frac{11}{13}\cdots\frac{4n-1}{4n+1}<\sqrt{\frac{3}{4n+3}}$

8 votes
Accepted

Elementary way to evaluate $\lim_{x\to0}\frac{\sqrt[n]{a+x} - \sqrt[n]{a-x}}{x}$

8 votes

Determinant is linear as a function of each of the rows of the matrix.

8 votes

Approximate solution: factorial and exponentials

8 votes

Intuition for the differences between characteristic and minimal polynomial

7 votes
Accepted

What is integer part of $\sum_{j=2}^{100}\frac{1}{\sqrt{j}}$?

7 votes

Ten books are to be arranged on a shelf. Permutation Question

7 votes
Accepted

Limit Evaluation - $\lim_{x\to \infty} \frac{1-e^x}{e^{2x}}$

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