Skip to main content

TL;DR

Convergence Toolbox: When Each Test Wins: A canonical quantitative trading interview question at intermediate difficulty. Commonly asked at Jane Street, HRT, Two Sigma.

By Valenke Exam Prep Team·Last updated 2026-06-01
intermediateSequences, Series & Limits

Convergence Toolbox: When Each Test Wins

Asked at: Jane Street, HRT, Two Sigma

Problem
Determine convergence or divergence of each series, choosing the most efficient test: (a) ∑n=1∞\ racn!nn\sum_{n=1}^{\infty} \ rac{n!}{n^n}, (b) ∑n=2∞\ rac1nln⁡2n\sum_{n=2}^{\infty} \ rac{1}{n \ln^2 n}, (c) ∑n=1∞\ rac(−1)nn\sum_{n=1}^{\infty} \ rac{(-1)^n}{\sqrt{n}}.
Related concepts
Series ConvergenceRatio Test

Ready to practice for the Valenke Finance Exam?

Adaptive practice powered by Item Response Theory targets your weak areas. Start with 3 free sessions.

Start free practice →
Practice similar problemsAll core problems