uni = Union[list, SameTest -> (Abs[#1 - #2] < 10^-4 &)]

[![enter image description here][1]][1]


    Total[Range[4, 1, -1] E^(uni/t)]

[![enter image description here][2]][2]


  [1]: https://i.sstatic.net/cDsdT.jpg
  [2]: https://i.sstatic.net/JVZ5Q.jpg