how do you prove a number is not triangular?

Question

i have to write an essay about triangular numbers and i need to know how to prove that a number is not triangular. it would help a lot!

Answer 1

Question: how do you prove a number is not triangular?

A number N is a triangular number if N (or Tn) = n(n+1)/2,

where Tn is called the nth triangular number.

Examples: T5 = 5*6/2 = 15, and T6 = 6*7/2 = 21.

A number N is not a triangular number if it lies somewhere between Tn and T(n+1), for some n.

E.g. 20 is not a triangular number because it lies between T5 and T6.