The sum of first n numbers where n is very large is calculated. What is the probability thai it is divisible by n?

a) 1
b) 3/4
c) 1/2
d) can't determine

• sum of n nos.= n(n+1)/2
  dividing it by n =n(n+1)/2n = (n+1)/2
  it is divisible by n if n+1 is even..
  so probability =1/2
• 10 years agoHelpfull: Yes(28) No(3)
• sum of 1st n numbers = n(n+1)/2
  
  as this is divisible by any value of n so the probability of it to be divisible by n would be 1.
  
  so coreect ans is (a)1
• 10 years agoHelpfull: Yes(10) No(12)
• Sum of 1st n numbers = n(n+1)/2
  
  This means that either n or (n+1) is divisible by 2
  
  (1)If n is divisible by 2,then S(n) will not be divisible by n because original value of n is reduced to half.
  
  But when n is not divisible by 2, this means that (n+1) is divisible by 2, and the originality of n is maintained
  
  i.e.
  
  let us assume (n+1)/2 = a
  
  S(n) = n(n+1)/2
  => n*a
  S(n) = n*a
  
  => n*a is divisible by n
  
  Hence Total probability = 1/2
• 10 years agoHelpfull: Yes(7) No(6)
• yuuppieee its 1/2
• 10 years agoHelpfull: Yes(4) No(1)
• rakesh bhai kaha ho
  solution do bhai
  
• 10 years agoHelpfull: Yes(4) No(2)
• Sum of 1st n numbers = n(n+1)/2
  now, n(n+1)/2n = (n+1)/2(dividing sum by n)
  Since, (n+1)/2 is divisible only if n is odd i.e. (n+1) is even.
  so probability must be 1/2.
• 10 years agoHelpfull: Yes(3) No(0)
• ans is (c) becz
  sum of 1st n numbers = n(n+1)/2
  We have to check when n(n+1)/2 is divisible by n
  Case 1: When n is even
  n(n+1) will be divisible by n resulting in (n+1) and since n is even (n+1) being odd will not be divisible by 2.
  Case 2: When n is odd
  n(n+1) will be divisible by n resulting in (n+1) and since n is odd (n+1) being even will be divisible by 2.
  So when n is very large, we have almost equal no of even and odd numbers.
  So the probability is 1/2.
• 10 years agoHelpfull: Yes(2) No(0)
• As it is said n is very large thus n+1~n so n*(n+1)~n*n what in that case n dividea or not
• 10 years agoHelpfull: Yes(0) No(1)
• since n is very large
  sum can be written as s = n(n+1)/2=(n^2)/2
  when devided by n q =n/2
  so probability will be 1
• 10 years agoHelpfull: Yes(0) No(0)
• sum of n numbrs= n(n+1)/2
  dividing it by n =n(n+1)/2=>n = (n+1)/2
  it is divisible by n if n+1 is even.............
  so probability is 1/2
• 10 years agoHelpfull: Yes(0) No(0)
• its obviously 1 becoz question ask it is divisible by n or not ...
  hw mny times u gonna divide the sum ..
  its surely 1
• 10 years agoHelpfull: Yes(0) No(0)