This article is outdated. Now indefinite sum is completely reduced to indefinite integral. To be sure of it look at http://www.oddmathes.info/indefinitesum . I recommend to begin with examples. There is at the bottom of a page a button “Examples”. In a drop-down menu click “Instruction”, read it and then open “Example1”. The example is a live one. You can insert an analytic function at your choice and calculate it. In the example there are detailed instructions in commentaries before each step. When you become sure that the formula works you can look at the article to see why it works.