Well....we couldn't calculate the sum of all of them....!!! {the sum would be infinite !!!}
But...we have a "formula" to calculate the sum of the first N of them.....
Let's take a simple example to see if we can find out what it is.......
Notice that.......if we had an some number of integers to add....we might have something like this.....
1 + 2 + 3 + .....+ N-2 + N-1 + N
Now, let's rewrite the same sum backwards and add both things......so we have
[ 1 + 2 + 3 +....... + N-2 + N-1 + N ]
+ [N + N-1 + N-2 + ..... + 3 + 2 + 1]
= [N + 1] + [N + 1] + [N + 1] + ..... +[N + 1] +[N + 1] +[ N + 1]
Now, notice that we have "N" pairs of [N + 1] terms.....so the sum of these is just ... N(N+ 1)
But.......we've summed the series twice.....so we need to divide the above result by 2
And we arrive at the "formula" for the sum of the first N integers......N(N + 1) / 2 ....... !!!!
