7777 books are to be placed in shelves such that the 1st shelf carry 1 book 2nd shelf 3 3rd shelf 6 4th shelf 10 5th shelf 15 books nd so on... how many shelves the books will require???

• It should be 7770
  1 - 1
  3 - (1 + 2)
  6 - (1 + 2 + 3)
  10 - (1 + 2 + 3 + 4)
  .
  .
  It is of the form n*(n+1)/2
  So nth shelf contains n*(n+1)/2 books
  Sum of books in all shelf => sum of n*(n+1)/2 terms
  Total books = 7770
  Sum of n*(n+1)/2 terms = 7770
  1/2*sum of [n^2 + n]
  Sum of n^2 terms = n(n+1)(2n+1)/6
  Sum of n terms = n(n+1)/2
  1/2*[n(n+1)(2n+1)/6 + n(n+1)/2] = 7770
  n(n+1)(2n+4)/12 = 7770
  n(n+1)(2n+4) = 7770*12
  n(n+1)(2n+4) = (2*3*5*7*37) * (2*2*3)
  n(n+1)(2n+4) = 35(2*2*3*3)(37*2)
  So n = 35
  
  Ans : 35
  
• 10 years agoHelpfull: Yes(15) No(1)
• 1,3,6,10,15---n*(n+1)/2
  and the sum of this series is
  1,4,10,20,35---n*(n+1)*(n+2)/6
  so the number of shelves will be 36 to fill 8436 books.
  but I think the question should be '7770 books' so that
  '35' shelves will be the answer
• 10 years agoHelpfull: Yes(2) No(5)
• the given series is in the form .. (n^2 + n)/2
  then sun of(n^2 + n)/2 = 7777. n= 35.
• 10 years agoHelpfull: Yes(1) No(4)
• plz confirm that dude wats the total number of book give 7770 or 7777
• 10 years agoHelpfull: Yes(0) No(0)