I add 2 ways more to solve this problem. The best method is way 3. The idea of this way, is "build floor" for remain element.
Consider array has n elements.
Step 0: Build floor for array[1], array[2], ... array[n] by add the value of array[0]
Step 1: Build floor for array[2], array[3], ... array[n] by add the value of array[1]
Step 2: Build floor for array[3], array[4], ... array[n] by add the value of array[2]
...
Step n-1: Build floor for array[n] by add the value of array[n-1]
And when finish this step, array[n] is the value you need last!  
//way1 = your way
function add(additem,arr){   
  return arr.map(x => x + additem);
}
function fold(input){
  if(input.length===1){
    return input[0];
  }
  else {
    var newArray=add(input[0],input.slice(1, input.length));
    if(newArray.length > 1){
      return fold(newArray); // return here               
    }      
    else{
      return newArray[0];
    }    
  }     
}
//way2
function way2(array){
    result = array;
    for(var i=0;i<result.length-1;i++){
      result = result.map(x=>x+result[i]);
    }
    return result[result.length-1];
}
//way3
function way3(array){
    var result = array;
    for(var i=0;i<result.length;i++)
      for (var j=i+1;j<result.length;j++)
        result[j] = result[i] + result[j];
    return result[result.length-1];
}
var arr=[2,5,4,3,1,3,4,9];
var sum=fold(arr);
console.log("Initial arr = " + arr);
console.log("way1 = the sum is: " + sum);
console.log("way2 = the sum is: " + way2(arr));
console.log("way3 = the sum is: " + way3(arr));