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Examples

(sum_{1 <= i <= 9} (x-i)²) = (x-1)² + (sum_{2 <= i <= 9} (x-i)²)

(sum_{1 <= i <= n} xⁱ) = (sum_{1 <= i <= n /\  iseven(i)} xⁱ) + (sum_{1 <= i <= n /\  isodd(i)} xⁱ)

Identities which are true for every x.