Calculas Limits?

Question

what is the answer for nEk=1 6k(k-1)/n^3?

Answer 1

By E do you mean Σ? You want the sum for k = 1 to n for the expression (6k² - 6k)/n^3? That will be (6 Σ k² - 6 Σ k)/n^3, and since Σk² = n(n+1)(2n+1)/6 and Σ k = n(n+1)/2, we get

6/6[2n^3 + 3n² + n]/n^3 - 6/2[n² + n]/n^3 =
2 + 3/n + 1/n² - 3/n - 3/n²,

and as n→∞, all terms approach 0 except the 2.

Answer 2

do u mean n to the power of k ?