# Addition of Consecutive Odd numbers is equal to Square Numbers

#### by Francis[ Edit ] 2012-12-01 17:23:02

**Addition of Consecutive Odd numbers is equal to Square Numbers**
**In this Square Table To Explain following Properties,**
1. Consecutive Odd number Addition is equal to consecutive square value.

2. A square number previous odd number is to multiply that number by 2 and separate by 1

3. A square number next odd number is to multiply that number by 2 and add by 1

** Example **
If you find 8

^{2},

Previous Odd Number is, 2*8 - 1 = 15

So that, 1 + 3 + 5 + 7 + 9 + 11 + 13 + 15 = 64

**Square Formula**:

**Proof**:

L.H.S = [((a

^{2} + b

^{2} + 2ab) + (a

^{2} + b

^{2} - 2ab) ) / 2] - b

^{2}
= [(2a

^{2} + 2b

^{2}) / 2] - b

^{2}
= [2(a

^{2}+b

^{2}) / 2] - b

^{2}
= (a

^{2}+b

^{2}) - b

^{2}
= a

^{2}
= R.H.S