Intereting Posts

Are there an infinite set of sets that only have one element in common with each other?
Plotting the locus of points equidistant from a point
Are proofs by contradiction really logical?
Prove $\text{rank}(A) \geq \frac{(\text{tr}(A))^2}{\text{tr}(A^2)}$ when $A$ is Hermitian
Under what circumstance will a covariance matrix be positive semi-definite rather than positive definite?
Recursive solutions to linear ODE.
What do we call well-founded posets whose elements have a unique height?
Isomorphism of two direct sums
Random diffusion coefficient in the Fourier equation
Prove that the intersection of two equivalence relations is an equivalence relation.
Global invertibility of a map $\mathbb{R}^n\to \mathbb{R}^n$ from everywhere local invertibility
How to evalutate this exponential integral
Prove by induction for $n \geq 1$, $x_n>x_{n+1} > \sqrt{R} $ and $ x_n- \sqrt{R} \leq \frac{1}{2^n} \cdotp \frac {(x_0- \sqrt{R})^2} {x_0} $
How to prove that the limit of an $n$-gon is a circle?
Question Concerning Vectors

Let $\zeta$ be the Riemann- Zeta function. For any integer, $n \geq 2$, how to prove $$\zeta(2) \zeta(2n-2) + \zeta(4)\zeta(2n-4) + \cdots + \zeta(2n-2)\zeta(2) = \Bigl(n + \frac{1}{2}\Bigr)\zeta(2n)$$

- Why must $a$ and $b$ both be coprime when proving that the square root of two is irrational?
- Logic and number theory books
- Prove that if a sequence $\{a_{n}\}$ converges then $\{\sqrt a_{n}\}$ converges to the square root of the limit.
- Finding two non-congruent right-angle triangles
- Proving a formula for $\int_0^\infty \frac{\log(1+x^{4n})}{1+x^2}dx $ if $n=1,2,3,\cdots$
- Can we prove that odd and even numbers alternate without using induction?
- How to use the method of “Hensel lifting” to solve $x^2 + x -1 \equiv 0\pmod {11^4}$?
- I would like to know an intuitive way to understand a Cauchy sequence and the Cauchy criterion.
- Are differences between powers of 2 equal to differences between powers of 3 infinitely often?
- Limit of a summation, using integrals method

This is too nice an exercise to give away. Your starting point should be:

$$\frac{t}{e^t-1} = 1 – t/2 + \frac{2 \zeta(2)}{(2 \pi)^2} t^2 – \frac{2 \zeta(4)}{(2 \pi)^4} t^4 + \frac{2 \zeta(6)}{(2 \pi)^6} t^6 – \cdots.$$

- $p = x^2 + xy + y^2$ if and only if $p \equiv 1 \text{ mod }3$?
- Computing the order of elements in Dihedral Groups
- How many different possible permutations are there with k digits that add up to n?
- How do you split a long exact sequence into short exact sequences?
- For finite abelian groups, show that $G \times G \cong H \times H$ implies $G \cong H$
- Can a number have both a periodic an a non-periodic representation in a non-integer base?
- The generating function for the Fibonacci numbers
- Rewriting repeated integer division with multiplication
- Under what conditions the quotient space of a manifold is a manifold?
- How to prove this series problem: $\sum_{r=1}^\infty \frac{(r+1)^2}{r!}=5e-1$?
- Relationship between rate of convergence and order of convergence
- Proving two entire functions are constant.
- How did we find the solution?
- For which cases with $2$ or $3$ prime factors do formulas for $gnu(n)$ exist?
- Does this sequence have any mathematical significance?