MathCastle
Counting & ProbabilityChallengeIdentities and Techniques, Proved

Identities and Techniques, Proved · Challenge problem

Evaluate ∑1≤i<j≤20(j−i)\displaystyle\sum_{1\le i<j\le 20}(j-i), the sum of j−ij-i over all pairs of integers with 1≤i<j≤201\le i<j\le20.