One of the most important parts of the documentation in Mathematica is the "See Also" (either the drop down menu at the top of the help window or the list at the bottom). If you go to a function that is close, you will likely find what you need quickly. For example if you ask for help for "Total" or "Plus", Accumulate is in Both of the "See Also" dropdowns. Wolfram Research did a good job in organizing this part of the documentation

Regards,

Neil

I find that the best way to get help is to use Google (or your favorite search engine). It’s often more useful than poring through the documentation. Chances are, you’re not the first person trying to figure out whatever it is you’re trying to do. For example, searching on “Mathematica partial sums of a series” goes right to Accumulate, and a lot of other good discussion.

The functional programming way to do it

FoldList[Plus, r]
(* {0, 1, 5, 8, 9, 12, 16, 24} *)

This guide page is worth studying.

Using AppendTo

m = 0;
result = {};
Do[AppendTo[result, m = m + r[[i]]], {i, 1, Length@r}];
result
(* {0, 1, 5, 8, 9, 12, 16, 24} *)

Using Sow and Reap, which is more efficient than AppendTo.

m = 0;
Do[Sow[m = m + r[[i]]], {i, 1, Length@r}] // Reap // Last // First
(* {0, 1, 5, 8, 9, 12, 16, 24} *)

Here is one way

r = {0, 1, 4, 3, 1, 3, 4, 8};
Accumulate[r]
(* {0, 1, 5, 8, 9, 12, 16, 24} *)