+0

Need help please ASAP

+1
47
1
+263

1) What is the smallest positive integer n such that the rightmost three digits of n! and (n+1)! are the same?

2)  $$N=1991\cdot1993\cdot1995\cdot1997\cdot1999.$$ What is the sum of the hundreds, tens and units digits of N?

3) What is the remainder when $$2+4+6+\cdots+100$$ is divided by 7?

Oct 24, 2020

#1
+1

1 - n = 10! =3,628,800  and (10+1)! = 11! =39,916,800

2 - N=1991*1993*1995*1997*1999 = N = 31601836203377055. Sum = 0 + 5 + 5 = 10

3 - sumfor(n, 1, 50, 2*n) = 2550 mod 7 = 2 - the remainder

Oct 24, 2020