there are 8436 steel balls each radius 1cm stacked on top of each other, 1 on the top layer, 3 on next layer, 6th in third, 10th in 4th and so on. How many horizontal layers are present?

• There is 1 ball on the top layer, (1+2) ball on the next layer, (1+2+3) ball in the next layer. So in Tn=(1+2+3...n)
  Tn=n(n+1)/2
  so Sum= summation of (n(n+1)/2)
  =summation of (n^2+n)/2
  =n(n+1)(2n+1)/12 + n(n+1)/4
  on solving, we get
  n(n+1)(n+2)/6= 8036
  n(n+1)(n+2)= 50616
  n(n+1)(n+2)=36*37*38
  so, n=36
• 9 years agoHelpfull: Yes(3) No(0)