I wish to compute
Sum[f[i], {i, 0, m}] - Sum[f[i], {i, 0, j}]
but can't get the expected result
Sum[f[i], {i, j+1, m}]
I also tried
Sum[f[i], {i, 0, m}] - f[0]
but can't get the expected result
Sum[f[i], {i, 1, m}]
It seems that mathematica can't change the minimum/maximum...