f[1, x_] := x^2

f[2,x_] := f[1,x]+x

f[3,x_] := f[2,x]+x

For[j = 1, j < 6, j++, f[j + 1, x] := f[j, x] + x]

$RecursionLimit::reclim2: Recursion depth of 1024 exceeded during evaluation of f[j,x].