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Michael Hartley's user avatar
Michael Hartley's user avatar
Michael Hartley's user avatar
Michael Hartley
  • Member for 10 years, 9 months
  • Last seen more than a month ago
9 votes
Accepted

If $a$ is a root of $x^2+ x + 1$, simplify $1 + a + a^2 +\dots+ a^{2017}.$

6 votes
Accepted

Fibonacci 19^n is multiple of 19 a mathematical property or a unique event?

4 votes

The sequence $(x_n)$ : $x_{n+2}=\frac{x_{n+1}\sqrt{x_n^2+1}+x_{n}\sqrt{x_{n+1}^2+1}-x_n-x_{n+1}}{x_{n+1}x_n-(\sqrt{x_{n+1}^2+1}-1)(\sqrt{x_n^2+1}-1)}$

4 votes
Accepted

Write all permutations in the cyclic group $C_{12}$ ​of order 12 in cycle notation.

4 votes
Accepted

Calculus Functional Equation

4 votes

Let $G$ be a group isomorphic to $Z_{n_1} \oplus Z_{n_2} \oplus \cdots\oplus Z_{n_k}$.

4 votes
Accepted

$a$ algebraic number, $\exists$ integer $n>0$ such that $na$ algebraic integer

4 votes
Accepted

Let $V$ be the space spanned by $v_1=\cos^2x$, $v_2=\sin^2x$ and $v_3=\cos2x$.

4 votes

If $450^\circ<\alpha<540^\circ$ and $\cot\alpha=-\frac{7}{24},$ calculate $\cos\frac{\alpha}{2}$. Why is my solution wrong?

4 votes
Accepted

Showing that either $v$ is an eigenvector for $2\times 2$ matrix $A$ or else $(A − \lambda \operatorname{Id})v$ is an eigenvector for $A$.

4 votes

If I flip two fair coins, and then tell you that one is heads, what is the probability that the other coin is also heads?

4 votes

A Number Theoretic Game

4 votes
Accepted

Proving the sum to product formula with complex numbers starting from the left hand side

3 votes
Accepted

What is the maximum number of distinct integers $A$ can have as elements?

3 votes

Powers of $2$ starting with $123$...Does a pattern exist?

3 votes
Accepted

Relation of surface area of a sphere to its volume.

3 votes

$P(X^2+Y^2<1)$ when $X,Y\sim U[0,1]$

3 votes

Coloring a rectangle with 3 rows and 4 columns using two colors.

3 votes

Finding Limit of an Integral: $\lim_{n\to\infty}\int_a^b f(x)\sin^3{(nx)} \:dx$

3 votes
Accepted

The number of real roots of an exponential equation with 4 parameters

3 votes
Accepted

Probability that exactly $3$ compartments have a passenger: what's wrong with my solution, how was the textbook answer obtained?

2 votes
Accepted

Prove that $\theta \cdot (x,y)=(x\cos(\theta),x\sin(\theta)+y\cos(\theta) )$ is an group action.

2 votes
Accepted

What is the largest number of elements of $\{\sin\alpha\cos\beta,\sin\beta\cos\gamma,\sin\gamma\cos\alpha\}$ (all angles acute) that can exceed $1/2$?

2 votes
Accepted

Prove that $\sum_{i=0}^{m}{\binom{n-i}{k}}=\binom{n+1}{k+1}-\binom{n-m}{k+1}$

2 votes
Accepted

Probability Distribution Calculation of Variables

2 votes
Accepted

Even integer has at least $K$ representations as the sum of two primes for any $K$

2 votes
Accepted

Help crafting equation - How to calculate all invalid combinations

2 votes

I have a mean and a desired range for a normal distribution, how do I discover what standard deviation I need?

2 votes

Rational numbers raised to an irrational power.

2 votes

solving this linear equation by substitution?