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You could define

def sums(a,nmax):
    return [sum(a[i] for i in xrange(n+1)) for n in xrange(nmax)]

Then you could compute for instance:

sage: a = [i^2 for i in xrange(20)]
sage: sums(a,10)
[0, 1, 5, 14, 30, 55, 91, 140, 204, 285]

Is that what you want, or do you want something that would take "symbolic lists" given by their names, and return a symbolic expression consisting in the formal sums of list elements? I'm not sure how one could do that.