Friday, October 9, 2009

Sum of k(k+1)(k+2)

Calculate 1*2*3 + 2*3*4 + 3*4*5 + ... + 998*999*1000.
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  1. DavidOctober 10, 2009 at 11:59 AM

    The answer is 249,499,750,500.

    Note that k(k+1)(k+2) = k(k+1)(k+2)(k+3)/4 - (k-1)k(k+1)(k+2)/4. When this expression is summed from k=1 to 998, all of the terms cancel except for 998*999*1000*1001/4 = 249,499,750,500.

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