How do you prove that 1 added to the product of 8 times a triangular number is a square number?

Answer 1

Any triangular number will have the form n(n+1)/2 for some integer n. Multiplying this number by 8 and adding 1, we obtain 4n²+4n+1, which is (2n+1)², a square number. Q.E.D.

Answer 2

1+8 x^3=1+2^3 1^3=1+8=9=3^2

Answer 3

formula=n(n+1)/2
Multiplying this number by 8 and adding 1
4n²+4n+1
which is (2n+1)², a square

Answer 4

You devise a formula for triangular numbers, you multiply it by 8 and add 1, then you simplify it.