<https://mathematica.stackexchange.com/a/222410/73364>
I have obtained the following code from the above link. But it is not working well with my situation. Can anyone help me out?



    SumHeld /: 
      SyntaxInformation[
       SumHeld] = {"LocalVariables" -> {"Table", {2, Infinity}}};
    
    IndexUnify[HoldPattern@Plus[sums : SumHeld[_, __] ..]] := 
     Plus @@ With[{targetIndices = List @@ #[[-1, 2 ;;, 1]], 
          sourceIndicesList = List @@@ #[[;; , 2 ;;, 1]]}, 
         Function[{sum, sourceIndices}, 
           sum /. Thread[
             sourceIndices -> 
              Take[targetIndices, Length@sourceIndices]]] @@@ 
          Transpose@{#, sourceIndicesList}] &@
      SortBy[Flatten /@ {sums}, Length]
    
    SumTogether[HoldPattern@Plus[sums : SumHeld[_, sameRanges__] ..]] := 
     SumHeld[Plus @@ {sums}[[;; , 1]], sameRanges]
    SumTogether[HoldPattern@Plus[sums : SumHeld[_, __] ..]] /; 
      UnsameQ @@ {sums}[[;; , 2 ;;]] := 
     Plus @@ SumTogether@*Plus @@@ GatherBy[{sums}, Rest]
Here please see the below test case. 

    test = SumHeld[f[a, i], {a, 1, 5}, {i, 1, 5}] + 
      SumHeld[SumHeld[2*f[b, j], {b, 1, 5}], {j, 1, 5}] + 
      SumHeld[SumHeld[2*f[c, j], {c, 1, 5}], {j, 1, 5}]
    % // IndexUnify
    % // SumTogether

The output I am receiving is

$$\text{SumTogether}\left(\sum _{c=1}^5 \sum _{j=1}^5 f(c,j)+2 \sum _{c=1}^5 \sum _{j=1}^5 2 f(c,j)\right)$$

Here the issue is it's not simplifying further as $$\left(\sum _{c=1}^5 \sum _{j=1}^55f(c,j)\right)$$

Another question is when I have more than 2 summation signs as below:

    test = SumHeld[f[a, i, j], {a, 1, 5}, {i, 1, 5}, {j, 1, 5}] + 
      SumHeld[SumHeld[2*f[b, j, i], {b, 1, 5}, {j, 1, 5}], {i, 1, 5}] + 
      SumHeld[SumHeld[2*f[c, j, i], {c, 1, 5}, {j, 1, 5}], {i, 1, 5}]
    % // IndexUnify
    % // SumTogether
Is the bracket I have placed correctly?