Competitions

Putnam proofs — Proofs

Putnam-level statements to prove in full. Name every theorem you use and check its hypotheses — that is what the graders reward.

Problem 1 of 21
Analysis

Prove that e=∑n=0∞1n!e=\sum_{n=0}^{\infty}\frac1{n!} is irrational.

Write a full proof on paper. There is no answer box — when you are ready, reveal the solution and compare your argument.

Proof practice — Putnam course