if 1!+2!+3!.....+50!is divided by 5!.what should be the remainder.

• In
  1!+2!+3!.....+50!
  
  all terms after 5! will have zero remainder when divided by 5!.
  sum of 1!+2!+3!+4! = 33
  
  when 33 is divided by 5! , we get 33 as remainder.
  
  so 33 is remainder .
• 11 years agoHelpfull: Yes(8) No(1)
• 33
  
  all terms after 5facorial are divisible by 5 factorial .therefore remainder is
  
  1+2+6+24 =33
• 11 years agoHelpfull: Yes(4) No(0)
• Lets first find the Sum of factorial,
  =1!+2!+3!+.....+50!
  =[1.1!+2.2!+3.3!+....+50.50!]/25*51
  =[(2-1).1!+(3-1).2!+(4-1).3!+......+(51-1).50!]/(25*51)
  =[2!-1!+3!-2!+4!-3!+..............._51!-50!}/(25*51)
  =[51!-1]/(25*51)
  =3.04*10^64
  if we divide S by 5!, remainder=4
• 11 years agoHelpfull: Yes(0) No(7)