proposition: the sum of the n least, positive, odd, integers is n^2. Which is the equation form of this?

Answer 1

If n=100, or n=99, the counting odd digits are 1,3,5,...,99 and adding them have 50².

What is your proposition exactly?

Answer 2

n=1, 1 = 1^2

n=2 1+3=4 =2^2

n=3 1+3+5 = 9 = 3^2

n=4 1+3+5+7 = 16 = 4^2

n=5 = 16+9=25=5^2

use sum of an arithmetic series formula, with d=2= common difference, a1=1= 1st term, an = nth term, n = any positive integer

sn =(n/2)(a1+an)= (n/2)(1+2n-1)=(n/2)(2n)= n^2= sum of n terms

an =a1+d(n-1)= 1+2(n-1)=2n-1= nth term