we have 1! +2! +3! + 4! +5! +6! +7x

where x is some number.. = 873+ 7x = 5+7y where y is some other num

(5+7y)=5mod7=-2mod7

so v have to hnik of  (-2)^500 mod7 to get reminder

whiv=ch is equal to 2^500mod7=(2^498)*4mod7=(8^166)*4 mod7

8=1mod7 so( 8)^166=1mod7

so 8^166*4=4mod7

so reminder is 4