TITLE: Sum of  n consecutive numbers
QUESTION [16 upvotes]: Possible Duplicate:
Proof for formula for sum of sequence $1+2+3+\ldots+n$? 

Is there a shortcut method to working out the sum of n consecutive positive integers?
Firstly, starting at $1 ... 1 + 2 + 3 + 4 + 5 = 15.$
Secondly, starting at any other positive integer ...($10$ e.g.): $10 + 11 + 12 + 13 = 46$.

REPLY [30 votes]: The rule, as given by Gerry's answer (and the generalization as per Henry's comment) can be easily visualized, in a similar way as we deduce the area of a rectangular trapezium: