=∑_(x=1)^n〖(3x)〗^2

Question

need to kow how to do this problem

Answer 1

=∑_(x=1)^n〖(3x)〗^2

S =∑_(x=1)^n (3x)^2   ( the sum, from x = 1 to x = n, of (3x)^2 )

S =9∑_(x=1)^n x^2

Now, ∑_(x=1)^n x^2 is the sum of the squares of the 1st n natural numbers and has a standard formula, S_n^2, where

S_n^2 = (n/6)(n + 1)(2n + 1)

Therefore, S = 9S_n^2

S = 1.5n(n + 1)(2n + 1)