APL:
+/⍳1E9
Try it yourself, download NARS2000 (free) here:
http://www.nars2000.org/
The "⍳" character is entered by typing ALT+i
Explanation:
1E9 is 1,000,000,000
⍳1E9 generates a vector containing integers from 1 to 1,000,000,000 (inclusive)
+/ is the sum of the vector
Any good APL interpreter will not actually generate a vector with a billion numbers but rather recognize the above expression and optimize the resulting operation for speed and minimal resource utilization.
EDIT:
Technically the "/" is the "reduction" operator acting along the last axis. In the case of a single dimensional array it acts along the only available axis. If, instead, it was acting on a matrix it would reduce along the columns. Here's a longer annotated example with output from the interpreter:
Generate a vector from 1 to 10:
⍳10
1 2 3 4 5 6 7 8 9 10
Sum:
+/⍳10
55
Generate a vector of ten one's and zero's, repeating until the end:
10⍴1 0
1 0 1 0 1 0 1 0 1 0
Now use that vector to reduce the original 1 to 10 vector, grabbing every other
element starting with the first. The effective result is that you end up with
all the odd numbers between 1 and 10:
(10⍴1 0)/⍳10
1 3 5 7 9
Same things, now grabbing the even numbers by flipping the 1 0 sequence to 0 1:
(10⍴0 1)/⍳10
2 4 6 8 10
Sum of all odd integers between 1 and 10:
+/(10⍴1 0)/⍳10
25
Sum of all even integers between 1 and 10:
+/(10⍴0 1)/⍳10
30
One could create a single vector with the odd integers between 1 and 10 followed by
the even integers between 1 and ten by simply concatenating the generating
expressions (APL executes from right to left):
((10⍴1 0)/⍳10),(10⍴0 1)/⍳10
1 3 5 7 9 2 4 6 8 10
And then you can reshape ("⍴") the result into a matrix:
2 5⍴((10⍴1 0)/⍳10),(10⍴0 1)/⍳10
1 3 5 7 9
2 4 6 8 10
Finally, use the scan operator again, now applied to a matrix, to sum along the
columns and produce a result for each row. The effect is to output a two element
vector with the sum of the odd integers between 1 and 10 as the first element
and the sum of all the even integers between 1 and 10 as the second:
+/2 5⍴((10⍴1 0)/⍳10),(10⍴0 1)/⍳10
25 30
If you want to try this type the lines immediately following my comments above right into the interpreter. The rho "⍴" or reshape operator is entered by typing ALT+r.
Hope this helps make sense of it. Of course, there are other ways to accomplish the same thing.
https://en.wikipedia.org/wiki/APL_syntax_and_symbols