# asymptotics

1. ### asymptotics

If $$\lim\limits_{n \to \infty} \dfrac{f(n)}{g(n)} = \dfrac{a}{b}$$ with $a \ne b$, $b \ne 0$ then $$b f(n) \sim a g(n)$$ ?....
2. ### Approximation near the singularity

Hi, I would like to somehow "approximate" function f(x) near its singularity p (f(p)=\infty) by a sum of powers of x. To be more precise, let f be function from R to R (real numbers - but if it would be more convenient, let's use complex numbers instead), let f had as "neat" properties as you...
3. ### asymptotics and recurrence

Let n_{0} \in \mathbb{N}, f,s: \mathbb{N} \rightarrow \mathbb{R} such that f(n) = f(n-1) + s(n), \forall n \geq n_{0} Prove by induction that if s(n) = O(n) then f(n) = O(n^{2})
4. ### Asymptotics

Hello. Here is the problem: f(m) = \sum_{k=2}^{m} \frac{1}{ln k!}. How to find f(m), where m \rightarrow \inf. I need your ideas:) Thanks