# Too many summations

Algebra Level 4

$\large \sum_{n=1}^j M_n = j, \sum_{n=1}^j A_n = j^2, \sum_{n=1}^j T_n = j^3, \sum_{n=1}^j H_n = j^4$

Given that $$M_n, A_n, T_n, H_n$$ are polynomials expressed in terms of $$n$$ such that the equations above holds true. If $$M_j + A_j +T_j + H_j = xj^3 - yj^2+yj + z$$ for constants $$x,y$$ and $$z$$, find the value of $$x+y+z$$.

×