Question Number 35723 by math2018 last updated on 22/May/18
$${Find}\:{the}\:{largest}\:{prime}\:{factor}\:{of}\:\:{the}\:{following}: \\ $$$$\left(\mathrm{1}×\mathrm{2}×\mathrm{3}\right)+\left(\mathrm{2}×\mathrm{3}×\mathrm{4}\right)+...+\left(\mathrm{2014}×\mathrm{2015}×\mathrm{2016}\right) \\ $$
Answered by MJS last updated on 23/May/18
$$\underset{{i}=\mathrm{1}} {\overset{{n}} {\sum}}\left({i}+\mathrm{2}\right)\left({i}+\mathrm{1}\right){i}=\frac{\mathrm{1}}{\mathrm{4}}\left({n}+\mathrm{3}\right)\left({n}+\mathrm{2}\right)\left({n}+\mathrm{1}\right){n} \\ $$$${n}=\mathrm{2014}\:\Rightarrow\:\mathrm{largest}\:\mathrm{prime}\:\mathrm{factor}\:={n}+\mathrm{3}=\mathrm{2017} \\ $$
Commented by math2018 last updated on 23/May/18
$${Thanks}\:{sir}! \\ $$