# Summation over list elements

As we know, one of the simplest way to do a summation (with special intervals) over list elements is using

Sum[list[[i]], {i, 3, 8, 2 }] (*with steps of 2*)


for a list such as list={a, b, c, d, e, f, g, h, i, j, k, l} which returns c + e + g.

How can we use Replacelist or FoldList to this aim?

I am learning important functions (FoldList and ReplaceList) which are used instead of (Accumulation) in sum over list, in which I faced to some problems and could not find correct things. Instead of accumulation, for a simple summation what does it work!?

• Why would you want to use a likely less efficient mechanism like ReplaceList or FoldList for this than what you've shown, or better yet, Tr@list[[3;;8;;2]]? Is this going to be a moving-goal-post question, and there's really something more complex you want to accomplish, or are you just looking for slower ways? – ciao Aug 11 '15 at 1:35
• @ciao You're starting to mind-read. Beware of what you find :) – Dr. belisarius Aug 11 '15 at 1:47
• "...you allow yourself to insult me...", huh? I have no idea what you're talking about. If I'd wanted to insult you (and I don't, no reason to and this is not the place for such nonsense in any case), I'd invite you to a chat room for a lashing... – ciao Aug 11 '15 at 5:19
• If I made mistake I do apologize, I am so sorry. Please pardon me, – Unbelievable Aug 11 '15 at 5:49

I'd allow myself some guesswork here, that you're going after alternatives as a form of excercise in Mathematica programming. However, you've clearly stated, that the list is

list={a, b, c, d, e, f, g, h, i, j, k, l}


and the expected output is

c + e + g


Note, that in the question you've linked, ReplaceList and FoldList are utilized to generate lists of results, analogous to Accumulate. But even then, the functions used in the replacement rules or passed as arguments to FoldList are the conventional Plus. In this question, only a single expression is expected.

Off the top of my head I can only come up with this improvement to your code:

Total@list[[3;;8;;2]]
(* c + e + g *)

• …and before Span[] became built-in, one used Take[]. – J. M.'s technical difficulties Aug 11 '15 at 13:37
• @Guesswhoitis. m[[i;;j;;k]] is equivalent to Take[m,{i,j,k}]. Interesting. I like to compare the FullForms: Part[list, Span[3, 8, 2]] or Take[list, List[3, 8, 2]]. They might as well have used a short form for Take. Can you say something regarding the performance of either function? – LLlAMnYP Aug 11 '15 at 13:41
• Not really much I can say ; to be honest, I tend to use Take[] more than Span[] as a force of habit. – J. M.'s technical difficulties Aug 11 '15 at 14:34