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The Gaussian Summation

Easy · Mental Math & Estimation · Quant Trader interview question · mental-math, arithmetic, series, gauss, interview-prep

This is a classic litmus test used in quantitative interviews to gauge mathematical literacy and historical awareness. Legend has it that Carl Friedrich Gauss solved this instantly in elementary school. Calculate the sum of all integers from 1 to 100 (inclusive): $$\sum_{i=1}^{100} i$$