I hope my computation is correct and the question is clear.
lim(n??)??(i=1)^n->(1/n^3(i-1)^2)
The instructions are:
use the properties of sigma notation to find a formula for the given sum of n terms. Then use the formula to find the limit as n---) oo
I am pasting from word so it might be a little dirty but I get this far;
=1/n^3 ?_(i=1)^n?(i-1)(i-1)
=1/n^3 ?_(i-1)^n?(i^2-2i-1)
=1/n^3 [?_(i=1)^n?i^2 -2?_(i=1)^n?i-?_(i=1)^n?1]
1/n^3 ([n(n+1)(2n+1)/6]-2[n(n+1)/2]-1(n) )
1/n^3 ([n(n+1)(2n+1)/6]-2[n(n+1)/2]-1(n) )???
The last line is a dup because at this point I am supposed to be plugging in a number but when I go to look for that number, it's an 'n' and at that point, well, just think "monkey with a lightbulb".
I know I am supposed to be testing the limit at this point but the end result is a whole number but I just don't see the connect.
lim(n??)??(i=1)^n->(1/n^3(i-1)^2)
The instructions are:
use the properties of sigma notation to find a formula for the given sum of n terms. Then use the formula to find the limit as n---) oo
I am pasting from word so it might be a little dirty but I get this far;
=1/n^3 ?_(i=1)^n?(i-1)(i-1)
=1/n^3 ?_(i-1)^n?(i^2-2i-1)
=1/n^3 [?_(i=1)^n?i^2 -2?_(i=1)^n?i-?_(i=1)^n?1]
1/n^3 ([n(n+1)(2n+1)/6]-2[n(n+1)/2]-1(n) )
1/n^3 ([n(n+1)(2n+1)/6]-2[n(n+1)/2]-1(n) )???
The last line is a dup because at this point I am supposed to be plugging in a number but when I go to look for that number, it's an 'n' and at that point, well, just think "monkey with a lightbulb".
I know I am supposed to be testing the limit at this point but the end result is a whole number but I just don't see the connect.