Paragraph: Consider the sum S =0!+1!+2!+3!+4!+ +100!34 Question: If the sum S is divided by 8 , what is the remainder?

Step-by-step solution

S=0!+1!+2!+ +100! Clearly all factorial from 4 to 100 have 4 2 i.e. 8 in them hence all of these are completely divisible by 8 . Remainder will be from 0!+1!+2!+3 ! =1+1+2+6=10 . After dividing 10 from 8 , remainder is 2