I need to prove that with math induction

Question

How to prove that

In secuence y_{n=(n-4)^2-1,  for n>= we have} 

Y_n+1>=y_n. 

Answer 1

y_n-1 = (n-5)² - 1

y_n = (n-4)² - 1

 

y_n - y_n-1 = (n-4)² - (n-5)²

  = n² -8n +16 - (n² -10n +25)

  = 2n - 9.

 

Whenever n > 4, this difference y_n - y_n-1 is therefore positive.  Q.E.D.