Sum of the first n odd integers?

Let's talk this out and see if we can work it out.

The sum of the first N odd integers means,

1+3+5+7+9+11+...

Where N is how many odd numbers we're adding.

Let's choose numbers for N, and see if we can find a pattern.

N=1 --> 1

(sum of the first odd integer)

N=2 --> 1 + 3 = 4

(sum of the first 2 odd integers)

N=3 --> 1 + 3 + 5 = 9

(sum of the first 3 odd integers)

N=4 --> 1 + 3 + 5 + 7 = 16

Do you notice a pattern yet? Take a look at when N = 2, what is the sum? That's right, 4!

and when N = 3... the sum is 9.

N = 4 the sum is 16....

I see a pattern, do you?

Answer: If you don't, you'll notice that the sum of the first N odd integers is always = N2