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A Bug in symbolic summation?


I wish to do a basic symbolic manipulation of two summations.
>      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}]


Though when I replace m with any definite number everything works
fine.

It seems that Mathematica can't change the minimum/maximum value of
the summation variable i above in symbolic calculation...


I also tried another system, but failed to do such symbolic computation.

Did I miss any point here?


Best,
Rex


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