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Evaluate

k = 1 5 k ( k + 1 ) ( k + 2 ) \sum_{k=1}^5 k(k+1)(k+2)


The answer is 420.

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1 solution

k = 1 5 k ( k + 1 ) ( k + 2 ) \sum_{k=1}^5k(k+1)(k+2) 1 ( 1 + 1 ) ( 1 + 2 ) + 2 ( 2 + 1 ) ( 2 + 2 ) + 3 ( 3 + 1 ) ( 3 + 2 ) + 4 ( 4 + 1 ) ( 4 + 2 ) + 5 ( 5 + 1 ) ( 5 + 2 ) 1(1+1)(1+2)+2(2+1)(2+2)+3(3+1)(3+2)+4(4+1)(4+2)+5(5+1)(5+2) 1 ( 2 ) ( 3 ) + 2 ( 3 ) ( 4 ) + 3 ( 4 ) ( 5 ) + 4 ( 5 ) ( 6 ) + 5 ( 6 ) ( 7 ) 1(2)(3)+2(3)(4)+3(4)(5)+4(5)(6)+5(6)(7) 6 + 24 + 60 + 120 + 210 = 30 + 60 + 330 = 90 + 330 = 420 6+24+60+120+210=30+60+330=90+330=\boxed{420}

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