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Default Summing a variable number of rows

I want to sum a variable number of rows which is in a column of numeric
information. For example, say the column has entries 1,2,3,4 and 5 in five
separate rows. I would like to be able to sum a number of contiguous entries
(e.g. sum the second, third and fourth rows, or sum the fourth and fifth
rows). This can obviously be done by creating a normal sum function (e.g.
=sum(A2:A4) for the first example above). However, if I want to vary where
the series is summed from (e.g. A2 or A3) - and the number of rows that are
summed (e.g. A2 to A4, or A4 to A5) - I need to go in and manually re-write
this formula. Is it possible to have a sum-type formula linked to two input
cells, where input cell one indicates where the summed series is to commence
from and cell two indicates the umber of rows that are to be summed?

Thanking you in advance.
 
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