summation

yellowho wrote:2 – 4 + 6 – 8 + 10 – 12 + . . . 994 – 996 + 998 – 1000 =

let's see multiple ways to do this.

(2 - 4) + (6 - 8) + (10 - 1 2) +...+ (994 - 996) + (998 - 1000)
-2 + (-2) + (-2) + ... + (-2) + (-2)
Now to find how many times we are adding -2, find the number of even integers between 2 and 1000, inclusive, and divide that number by 2.
Number of even integers between 2 and 1000, inclusive = 1000/2 = 500, but number of times we are adding -2 is half of 500, that is 250.
So, 2 – 4 + 6 – 8 + 10 – 12 + . . . 994 – 996 + 998 – 1000 = (-2) * 250 = -500