(There is a formula. I have a poor memory for formulas but am good at transforming English into them, so I just remember the English gloss.)

I'm decently impressed that Wolfram was able to spit out something equivalent to the right formula with only a little massaging of the inputs from me:

http://www.wolframalpha.com/input/?i=sum+of+n+from+n%3Da+to+...

  (loop for x from 1 to 365 summing x)  ==> 66795

Unless you want it for this: http://www.wolframalpha.com/input/?i=sum+of+n+from+1+to+n

  (reduce + (range 366))

  reduce (operator.add, range(366))

   sum(range(366))

  (sum (range 1 365))

  (defun range (start end)
    (loop for x from start to end collecting x))

  (defun sum (sequence)
    (reduce #'+ sequence))

Math/brain fail.