Question Number 35005 by Rasheed.Sindhi last updated on 14/May/18
$$\mathrm{Find}\:\mathrm{remainder}\:\mathrm{when} \\ $$$$\:\:\:\:\mathrm{1}!+\mathrm{2}!+\mathrm{3}!+...+\mathrm{99}!+\mathrm{100}! \\ $$$$\mathrm{is}\:\mathrm{divided}\:\mathrm{by}\:\:\mathrm{12}. \\ $$
Answered by rahul 19 last updated on 14/May/18
$$\mathrm{9}\:. \\ $$$${yes}\:{did}\:{the}\:{same}\:{way}\:{as}\:{done}\:{by}\: \\ $$$${mjs}\:{sir}. \\ $$
Commented by Rasheed.Sindhi last updated on 14/May/18
$$\mathrm{Right}! \\ $$
Commented by rahul 19 last updated on 14/May/18
☺️☺️
Answered by MJS last updated on 14/May/18
$$\mathrm{since}\:\mathrm{4}!=\mathrm{24}\Rightarrow\mathrm{remainder}\:\mathrm{of}\:\left(\underset{{n}=\mathrm{4}} {\overset{\infty} {\sum}}{n}!\right)/\mathrm{12}\:\mathrm{is}\:\mathrm{zero} \\ $$$$\mathrm{so}\:\mathrm{we}'\mathrm{re}\:\mathrm{looking}\:\mathrm{for}\:\mathrm{the}\:\mathrm{remainder}\:\mathrm{of} \\ $$$$\left(\mathrm{1}!+\mathrm{2}!+\mathrm{3}!\right)/\mathrm{12}=\mathrm{9}/\mathrm{12}\:=\mathrm{9} \\ $$
Commented by Rasheed.Sindhi last updated on 14/May/18
†håñk§ §ïr!