You can put this solution on YOUR website! the greatest triangular number less than 5000.
T(sub n) = (n(n+1))/2
this is also sum of all natural (counting numbers) from 1 to n
n(n+1) < 10000
10000 = 100^2
100 * 101 = 10100
99 * 100 = 9900
9900/2 = 4950
T(sub 99) = 4950 largest triangular number less than 5000