use the recursion relation to solve

Question

Determine a recursion relation H(n), including any initial conditions, for the total number of hockey balls in a pile with n layers where the sum of first positive integers is H(n)= n(n+1)/2 the layers are like 1,3,6

Answer 1

H(n+1)=(n+1)(n+2)/2.

H(n+1)/H(n)=(n+1)(n+2)/2÷n(n+1)/2=(n+2)/n.

Therefore H(n+1)=(n+2)H(n)/n and H(1)=1.