Please explain the concept used in the problem Sums in a Triangle the links to the problem is https://www.codechef.com/problems/SUMTRIAN and kindly enlighten me withe concept used.

You already used the tag "dynamic programming’ . So i think you know the basic fundamental. What exactly do you need help with???

I will show you a recursive method to solve the problem.
where if i is last row than ans(i,j)=M[i][j]
just call for ans(0,0)