New posts in Asymptotics

Prove that $\sum_{i=1}^{n}\frac{1}{\left(n+i\right)^{2}}\sim\frac1{2n}$

Prove the asymptotic for the sum $\sum_{d\mid n}\frac{\mu(d)\ln(d)}{d}=O(\ln(\ln(n)))$

How many numbers $n$ are there such that $\gcd(n,\phi(n)) = 1$?

Summation of fractional parts of $x/n$

Little-o notation: limit in the definition

Asymptotic behaviour of $f(x) = \sum_{n=1}^\infty n^\varepsilon \frac{x^n}{n!}$ for $\varepsilon\in(0,1)$

How does $a^{a^n}$ compare with $n!$ asymptotically?

Does a general formula for $\sum_{r=1}^{n}r^k$ proof exist?

Do I have a chance to get a closed form for this integral?

Asymptotic expansion of $u_{n + 1} = \frac12 \arctan(u_n)$