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Counting & ProbabilityEasyIdentities and Techniques, Proved

Identities and Techniques, Proved · Easy problem

Every positive integer kk satisfies k2=2(k2)+(k1)k^2=2\binom{k}{2}+\binom{k}{1}. Use this and the hockey stick identity to find 12+22+32+⋯+1221^2+2^2+3^2+\cdots+12^2.