Intereting Posts

Explanation/How to use the Lattice isomorphism theorem
Counting $x$ where $an < x \le (an+n)$ and lpf($x$) $ \ge \frac{n}{4}$ and $1 \le a \le n$
positive martingale process
Motivation for Napier's Logarithms
Why is the area under a curve the integral?
Solution of Differential equation $\frac{xdx-ydy}{xdy-ydx} = \sqrt{\frac{1+x^2-y^2}{x^2-y^2}}$
What does it mean for a set to exist?
How to calculate the percentage of increase/decrease with negative numbers?
Prove by induction that $n^5-5n^3+4n$ is divisible by 120 for all n starting from 3
For a field $K$, is there a way to prove that $K$ is a PID without mentioning Euclidean domain?
The series expansion of $\frac{1}{\sqrt{e^{x}-1}}$ at $x=0$
Martingale theory to show f(x+s) = f(x)
$\mathbb{A}^{2}$ not isomorphic to affine space minus the origin
$(0,1)$ is an open subset of $\mathbb{R}$ but not of $\mathbb{R}^2$, when we think of $\mathbb{R}$ as the x-axis in $\mathbb{R}^2$. Prove this.
About the ratio of the areas of a convex pentagon and the inner pentagon made by the five diagonals

If $\lim_{n\to \infty} (3^n + 4^n)^{1/n} = 4$, then $\lim_{n\to \infty} 3^n + 4^n=\lim_{n\to \infty}4^n$ which implies that $\lim_{n\to \infty} 3^n=0$ which is clearly not correct. I tried to do the limit myself, but I got $3$. The way I did is that at the step $\lim_{n\to \infty} 3^n + 4^n=\lim_{n\to \infty}L^n$ I divided everything by $4^n$, and got $\lim_{n\to \infty} (\frac{3}{4})^n + 1=\lim_{n\to \infty} (\frac{L}{4})^n$. Informally speaking, the $1$ on the LHS is going to be very insignificant as $n \rightarrow \infty$, so $L$ would have to be $3$. Could someone explain to me why am I wrong and how can the limit possibly be equal to $4$? Thanks!

- Evaluating $\sum_{n=0}^{\infty } 2^{-n} \tanh (2^{-n})$
- Prove $3^n = \sum_{k=0}^n \binom {n} {k} 2^k$
- Is differentiating on both sides of an equation allowed?
- Is there any integral for the Golden Ratio?
- Number of solutions of Frobenius equation
- Prove that $ \int \limits_a^b f(x) dx$ = $ \int \limits_a^b f(a+b-x) dx$
- Evaluate $\lim \limits_{n\to \infty }\sin^2 (\pi \sqrt{(n!)^2-(n!)})$
- Finding the angle between two line equations
- Global maximum and minimum of $f(x,y,z)=xyz$ with the constraint $x^2+2y^2+3z^2=6$ with Lagrange multipliers?
- Show that, for all $n > 1: \frac{1}{n + 1} < \log(1 + \frac1n) < \frac1n.$

$\infty-\infty$ is not well-defined.

- How to prove that no constant can bound the function f(x) = x
- $p$ prime, $1 \le k \le p-2$ there exists $x \in \mathbb{Z} \ : \ x^k \neq 0,1 $ (mod p)
- In a one-to-many relationship, how to find the minimum set of “ones” needed to get all of the “manys”?
- Brownian motion – Hölder continuity
- Can I represent groups geometrically?
- Prove that $d^2x/dy^2$ equals $-(d^2y/dx^2)(dy/dx)^{-3}$
- Complicated exercise on ODE
- Number of couples sitting at same table
- Functional Analysis: The rank of an operator detemines if it's a compact operator.
- Say $X$ is $T_2$, $f: X \to Y$ is continuous, $D$ is dense in $X$ and $f|_D :D \to f(D)$ is a homeomorphism. Then $f(D) \cap f(X- D) = \emptyset$
- $\displaystyle\sum_{k=0}^n \frac{\cos(k x)}{\cos^kx} = ?$
- Lack of homeomorphism between compact space and non-Hausdorff space
- Fixed-time Jumps of a Lévy process
- How to plot a phase potrait of a system of ODEs (in Mathematica)
- Behavior of $u\in W_0^{1,p}(\Omega)$ near the boundary.