Finite (and infinite!) sums occur with such frequency in mathematics that special notation has been developed. (Sorry, full inline mathematical notation does not yet exist for most HTML browsers). I will write SUM_i=mⁱ⁼ⁿ (a_i) = a_m + ... + a_n instead!

Summation is linear in that

SUM (a_i + b_i) = SUM a_i + SUM b_i.
SUM (a_i - b_i) = SUM a_i - SUM b_i.
c SUM a_i = SUM (c a_i)

Certain sums are very easy to compute, for example

SUM_i=1ⁱ⁼ⁿ ( 1 ) = n
SUM_i=1ⁱ⁼ⁿ ( i ) = n(n+1)/2
SUM_i=1ⁱ⁼ⁿ ( i² ) = n(n+1)(2n+1)/6

Last modified Wed Nov 6 23:04:49 CST 1996