Intereting Posts

Proving that there are at least $n$ primes between $n$ and $n^2$ for $n \ge 6$
Colorful squares arrangement
a simple recurrence problem
Prove by induction that $10^n -1$ is divisible by 11 for every even natural number
Prove that the maximum value of $|\vec{a}-\vec{b}|^2+|\vec{b}-\vec{c}|^2+|\vec{c}-\vec{a}|^2$ is $9$
Construct a finite field of order 27
How many numbers less than $x$ have a prime factor that is not $2$ or $3$
What is the correct value of $\pi$
Best representation of a polynomial as a linear combination of binomial coefficients
Let $n \in \mathbb{Z}^+$, prove the identity $ \sum_{k=1}^{n-1} \binom {n} {k} \frac{kn^{n-k}}{k+1}=\frac{n(n^{n}-1)}{n+1}$
No extension to complex numbers?
Permutation Partition Counting
interpretation of SVD for text mining topic analysis
Orthogonal Decomposition
Questions about proof of $\lim x_n = a, \lim y_n = b\implies \lim x_n+y_n = a+b$ in a normed vector space

Find the limit $$\lim_{n\to \infty} {a^n-b^n\over a^n+b^n}.$$ How do I find this limit? Thank you.

- $C^\infty$ approximations of $f(r) = |r|^{m-1}r$
- If $f'(x) = 0$ for all $x \in \mathbb{Q}$, is $f$ constant?
- Evaluate $\int_{0}^{\infty}\frac{\alpha \sin x}{\alpha^2+x^2} \mathrm{dx},\space \alpha>0$
- There is a unique polynomial interpolating $f$ and its derivatives
- Evaluating the primitive $\int \frac{\mathrm dx}{e^{2x} + e^x + 1} $
- Easy way of memorizing or quickly deriving summation formulas
- Evaluate $\int e^{2\theta} \sin (3\theta)\ d\theta$
- What is $\int_0^1\frac{x^7-1}{\log(x)}\mathrm dx$?
- Explicit value for $\sum_{n=1}^{\infty} \left(\frac{1}{\sqrt{1}+\sqrt{2}+\dots+\sqrt{n}}\right)$
- Proof of Frullani's theorem

Look at the possible cases $|a|=|b|$; $|a|<|b|$ or $|a|>|b|$.

The intuition here is that as $n$ grows, the larger of $|a|$ or $|b|$ will grow much faster than the smaller. It will come to dominate both the numerator and denominator, so you should be able to guess the limit by ignoring the smaller one. Once see the intuition and have a statement you want to prove, you should be able to find the limit using techniques you’ve seen before.

- If $I$ is countable, $\tau$ is a stopping time iff $\forall t\in I, (\tau=t)\in \mathcal F_t$
- How to find $A$ from $Ax=b$?
- Showing $$ is nilpotent.
- Integral of sine multiplied by Bessel function with complicated argument
- Ascending chain conditions on homogeneous ideals
- Correlation in Bernoulli trial
- Dimensions of a box of maximum volume inside an ellipsoid
- Any quotient group of $(\mathbb Q,+)$ is torsion
- What is “Russian-style” mathematics?
- When should I use $=$ and $\equiv$?
- How to prove that a union of a countably infinite set and a finite set is countably infinite with no intersection
- How to find the projw(x)
- Determine y-coordinate of a 3rd point from 2 given points and an x-coordinate.
- Proof $\int_0^\infty \frac{\exp(-\sqrt{x^2+y^2})}{x^2+y^2}dx = \frac{\pi}{2}\left(\frac{1}{y} – K_0(y)L_{-1}(y) – K_1(y)L_{0}(y)\right)$
- What's so special about the group axioms?