1. annoying sigma problem

I have done it a few times, but I can't seem to get the right answer:

Limit n-> infinity : nE(i=1)_(1+(2i)/n)^2*(2/n)

here is my best attempt:

(limit in front for all of this)
1. move the 2/n over to get: 2/n*(nE(i=1)_(1+(2i)/n)^2)
2. foil to get: 2/n*(nE(i=1)_(1+4i/n+4i^2/n^2)
3. break it put into further sigma: 2/n*(nE(i=1)_1+nE(i=1)_4i/n+nE(i=1)_4i^2/n^2)
4. move over shit: 2/n*(nE(i=1)_1+(4/n)*nE(i=1)_i+(4/n^2)*nE(i=1)_i^2)
5. simplify the sigmas: 2/n*(n+(4/n)*((n)(n+1)/2)+(4/n^2)*((n)(n+1)(2n+2))/6))
6. simplifying: 2/n*(n+2(n+1)+(2*(n+1)(2n+2)/(3*n)))

at this point I am not quite sure what to do to be honest, I am not sure how to simplify the 3rd term more tied in with the front 2/n

any ideas?

2. That looks complicated.

3. i dont know what you're talking about?

are the E's supposed to be summation signs? who calls them sigmas? ill try to make sense of how you're writing the notation.

4. lol yes they are summation, I call them sigmas

5. (4/3)n^2 + 4n + 6

6. assuming i interpreted that clusterfuck of a problem correctly

7. what the fuck

8. hold the fuck up kirby, is this the problem?

lim n->infinity, summation from i=1 to n of ((1+(2i/n))^2) * (2/n)

9. uh what are the limits of summation. i=1 to infinity? whats does the n in front of the sum mean, a constant?

10. yeah

11. he means the n is on top of the sigma which he represents by E. so its i=1 to n.

12. Originally Posted by Kirby
yeah
ok hold on

13. Originally Posted by God
uh what are the limits of summation. i=1 to infinity? whats does the n in front of the sum mean, a constant?
basically 1 to infinity, the n works for the format for some reason, basically at the end of this problem you substitute infinity to n

in reality the problem looks like this
...................................n
lim .............................E........the problem
n->infinity ...................i=1

14. 26/13

15. it says no

16. fuck i meant 26/3

17. i havent done a sum problem in a while but just with some preliminary scribbling, is it just 4?

18. rayne got it

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