Let #a_n# be a sequence given by: #{1, 6, 15, 28, 45,66,..., f(n)}#. Show that the generating function #f(n)# is of the form # an^2 + bn + c#. Find the formula by computing the coefficients #a, b, c#?
1 Answer
Explanation:
Strategy:
Take the given sequence find the difference between consecutive numbers:
Step 1
Step 2
Taking the difference is in discrete math is the same as taking the derivative (i.e. slope). took two subtraction (two layers) before we reached a comstant number
Give that I asert that:
All I have to do now find the value of
To solve for
Solving a, b, c using any matrix calculator on the internet:
Check:
PS: You can also use python, I used python simply... It is cool