If N is odd you add all odd numbers 1 to N and if N is even you add all even numbers 2 to N so according to this what is 2009 minus 2008 and how did you do that?

Answer 1

The formula for the sum of the odd number from 1 to N is N2
The sum of the even numbers form 2 to N is N(N+1)

Here are examples of each to see how they work.
Let's look at 1-5
The odd numbers are 1,3, an 5 and their sum is 9 which is the sum of the first THREE odd numbers so it is 32
The evens are 2,4 and their sum is 6 which is the sum of the first TWO even numbers so it is 2x3

9-6=3 which is the sum of the odd minus the evens.

Let N be the odd number then N-1 is the even number. In the example N=2009 and N-1=2008.

First in the simple example we have 5 and 4. To see how many odd numbers there are between 1 and 5, take 5 divided by 2= 2.5 and take the great the least integer greater than that which is 3. Take the greatest integer less than 2.5=2 to find the number of even number.

So 2009/2=1004.5 so we have 1005 odd numbers between 1 and 2009
Now for 2008, divide that by 2 =1004 and that is how many even numbers there are between 2 and 2008 inclusive.

Now 1005-1004=1
But you may want 10052 -(1008)(1009)=-7047