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f = a \[Function] 
   With[{A = UpperTriangularize[Outer[Plus, Join[{0}, -Most[#]], #, 1] &[Accumulate[a]]]},
    MaximalBy[
      Flatten[MapIndexed[{x, i} \[Function] {x, i}, A, {2}], 1], 
      First
      ][[1]]
    ];

{sum, pos} = f[{1, 2, 3, 4, 5, -1, 7, -4, -2}]

{21, {1, 7}}

f = a \[Function] 
   With[{A = UpperTriangularize[Outer[Plus, Join[{0}, -Most[#]], #, 1] &[Accumulate[a]]]},
    MaximalBy[
      Flatten[MapIndexed[{x, i} \[Function] {x, i}, A, {2}], 1], 
      First
      ][[1]]
    ];

{sum, pos} = f[{1, 2, 3, 4, 5, -1, 7, -4, -2}]

{21, {1, 7}}

f = a \[Function] 
   With[{A = UpperTriangularize[Outer[Plus, Join[{0}, -Most[#]], #, 1] &[Accumulate[a]]]},
    MaximalBy[
      Flatten[MapIndexed[{x, i} \[Function] {x, i}, A, {2}], 1], 
      First
      ][[1]]
    ];

{sum, pos} = f[{1, 2, 3, 4, 5, -1, 7, -4, -2}]

{21, {1, 7}}

f = a \[Function] 
   With[{A = UpperTriangularize[Outer[Plus, Join[{0}, -Most[#]], #, 1] &[Accumulate[a]]]},
    MaximalBy[
      Flatten[MapIndexed[{x, i} \[Function] {x, i}, A, {2}], 1], 
      First
      ][[1]]
    ];

{sum, pos} = f[{1, 2, 3, 4, 5, -1, 7, -4, -2}]

{21, {1, 7}}

f = a \[Function] 
   With[{A = 
      UpperTriangularize[
       Outer[Plus, Join[{0}, -Most[#]], #, 1] &[Accumulate[a]]]},
    MaximalBy[
      Flatten[MapIndexed[{x, i} \[Function] {x, i}, A, {2}], 1], 
      First][[1]]
    ];

{sum, pos} = f[{1, 2, 3, 4, 5, -1, 7, -4, -2}]

{21, {1, 7}}

f = a \[Function] 
   With[{A = UpperTriangularize[Outer[Plus, Join[{0}, -Most[#]], #, 1] &[Accumulate[a]]]},
    MaximalBy[
      Flatten[MapIndexed[{x, i} \[Function] {x, i}, A, {2}], 1], 
      First
      ][[1]]
    ];

{sum, pos} = f[{1, 2, 3, 4, 5, -1, 7, -4, -2}]

{21, {1, 7}}