Find the largest prime factor of the following: (1×2×3)+(2×3×4)+...+(2014×2015×2016)


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Question Number 35723 by math2018 last updated on 22/May/18

$F i n d t h e l a r g e s t p r i m e f a c t o r o f t h e f o l l o w i n g :$ $(1 \times 2 \times 3) + (2 \times 3 \times 4) + . . . + (2014 \times 2015 \times 2016)$
	Answered by MJS last updated on 23/May/18

	$\underset{i = 1}{\sum^{n}} (i + 2) (i + 1) i = \frac{1}{4} (n + 3) (n + 2) (n + 1) n$ $n = 2014 \Rightarrow largest prime factor = n + 3 = 2017$
	Commented by math2018 last updated on 23/May/18

	$T h a n k s s i r!$
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