Intereting Posts

How does atan(1) * 4 equal PI?
Number of positive, negative eigenvalues and the number of sign changes in the determinants of the upper left submatrices of a symmetric matrix.
Choosing half of prefix and suffix
If $(y_{2n}-y_n) \to 0$ then $\lim_{n\to \infty} y_n$ exists
Category of Field has no initial object
Jacobian matrix
How to compute $S_{2016}=\sum\limits_{k=1}^{2016}\left(\sum\limits_{n=k}^{2016}\frac1n\right)^2+\sum\limits_{k=1}^{2016}\frac1k$?
Exist $\alpha < \infty$, $\beta > 0$ such that $\mathbb{P}\{T_\lambda > t\} \le \alpha e^{-\beta t}?$
A game of guessing a chosen number
What is known about the minimal number $f(n)$ of geometric progressions needed to cover $\{1,2,\ldots,n\}$, as a function of $n$?
Free Throw Probability and Expected Number of Points
Is the closure of $ X \cap Y$ equal to $\bar{X} \cap \bar{Y}$?
In (relatively) simple words: What is an inverse limit?
Conditions that ensure that the boundary of an open set has measure zero
If $S$ is a finitely generated graded algebra over $S_0$, $S_{(f)}$ is finitely generated algebra over $S_0$?

I tried this form:

$$\lim_{n\to+\infty}\left(\prod_{x=2}^{n}\frac{\left(x-1\right)\left(x^2+x+1\right)}{\left(x+1\right)\left(x^2-x+1\right)}\right)$$ but it doesn’t ring any bell.

- Integrating $\int \sin^n{x} \ dx$
- Integral involving Gauss Hypergeometric function, power, exponential and Bessel Function
- How to prove $\int_0^{2\pi} \ln(1+a^2+2a\cos x)\, dx=0$?
- nonstandard example of smooth function which fails to be analytic on $\mathbb{R}$
- What is the formula for nth derivative of arcsin x, arctan x, sec x and tan x?
- Segment ordered density conjecture revisited
- Useful examples of pathological functions
- Calculate in closed form $\int_0^1 \int_0^1 \frac{dx\,dy}{1-xy(1-x)(1-y)}$
- What is $\lim_{n\to\infty}2^n\sqrt{2-\sqrt{2+\sqrt{2+\dots+\sqrt{p}}}}$ for $negative$ and other $p$?
- A polynomial agreeing with a function and its derivatives

Write out the fraction

$\frac {(x-1)(x^2+x+1)}{(x+1)(x^2-x+1)} $

for $x\in \{2,3,…,10\} $. Multiply these together and note that most factors cancel; **you have a telescoping product**. Once you figure out how the product telescopes, you can extrapolate to $n\rightarrow \infty $ and extract the terms at the “front end” of the telescope to get the limit.

- Riemannian metric in the projective space
- Properties of finite magmas $(S,\cdot)$ with $\forall(x,y,z)\in S^3, x\cdot(y\cdot z)=y\cdot(x\cdot z)$?
- Find all real real functions that satisfy the following eqation $f(x^2)+f(2y^2)=$
- Evaluate the following integral $\int_{0}^{10}\sqrt{-175e^{-t/4}+400}dt$
- An expression for $U_{h,0}$ given $U_{n,k}=\frac{c^n}{c^n-1}(U_{n-1,k+1})-\frac{1}{c^n-1}(U_{n-1,k})$
- Calculating $\lim_{x\to-\infty}\left(\sqrt{4x^2-6}-\sqrt{4x^2+x}\right)$
- Infinite subset of Denumerable set is denumerable?
- Nowhere monotonic continuous function
- How to solve infinite repeating exponents
- Why can't epsilon depend on delta instead?
- Path-connected and locally connected space that is not locally path-connected
- What is the probability that $X<Y$?
- “faces” of a non-planar graph
- Proof that $a\equiv 1\,(\textrm{mod }8)$ implies $a$ is a square modulo $2^n$ for all $n$
- Characteristic 2