Find-the-largest-prime-factor-of-the-following-1-2-3-2-3-4-2014-2015-2016-

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) + \dots + (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!