Little Gauss v2?

Proving the sum-of-integers formula

This is a cooked puzzle that tests your ability to construct a clear, rigorous proof of a foundational result in mathematics. It appears simple on the surface, but interviewers use it to assess how you think about induction, algebraic manipulation, and mathematical communication—all critical in quantitative roles where you need to justify claims about models and algorithms.

The question asks you to prove a closed-form formula for the sum of the first n positive integers. Success hinges on choosing a proof strategy (there are several valid approaches), executing it without logical gaps, and explaining each step clearly. Candidates who can move fluidly between concrete examples, pattern recognition, and formal argument tend to score well here.

• Mathematical induction and base/inductive cases
• Algebraic rearrangement and simplification
• Closed-form vs. recursive representations