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Find the closed form sum of 1*2*3 + 2*3*4 + 3*4*5 + ... + n(n + 1)(n + 2).

 Nov 27, 2020
 #1
avatar+9185 
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\(\sum\limits_{k=1}^{n}(k)(k+1)(k+2)\) .

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 Nov 27, 2020
 #2
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The "closed form" of the sequence is:

 

a_n = n^3 + 3 n^2 + 2 n 

 Nov 27, 2020
 #3
avatar+31703 
+2

Not exactly a derivation, but

 

 

It can be proved by induction.

 Nov 28, 2020
edited by Alan  Nov 28, 2020

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