Husk, 10 bytes
Fż+So:`R0C
Ungolfed/Explanation
-- implicit inputs n & xs | 3 [1,2,3,4]
S C -- cut xs into sublists of length n & ... | [[1,2,3], [4]]
(:`R0) -- ... prepend [0,...,0] (length n) | [[0,0,0], [1,2,3], [4]]
F -- accumulate the sublists with |
ż+ -- element-wise addition | [0+1+4, 0+2, 0+3]