Sunday, September 17, 2017

q: the sum of odd numbers

The sum of sequential odd numbers starting from 1 is a square number.
Examples:

1+3=4 (or 2 squared)
1+3+5=9 (or 3 squared)
1+3+5+7=16 (or 4 squared)
1+3+5+7+9=25 (or 5 squared)
1+3+5+7+9+11=36 (or 6 squared)

Question 1:
Is this always true?

Question 2:
Why?

Posted by at

2 comments:

  1. Vardaan's MaSeptember 17, 2017 at 7:45 PM

    Q1 yes
    Q2 as the difference between the consecutive squares is always 2n + 1, it translates to consecutive odd numbers. Eg. Difference between 2 squared and 3 squared is 5. Which is 2x2+ 1

    ReplyDelete
  2. Philip NgaiSeptember 21, 2017 at 11:11 AM

    Very good!

    ReplyDelete

Subscribe to: Post Comments (Atom)