Question

Need help with a limit/integral problem

http://puu.sh/6u228.jpg

I have no clue what to do

Answer 1

first expand

Answer 2

then break up the summation in to three parts
then pull the terms with n outside the sum, because the index is i not n

Answer 3

can you show me? I'm new to this

Answer 4

if the latex was working i could write it, but i cannot

Answer 5

let me write in a document, and attach it

Answer 6

although the first step, expanding, i am sure you can do
i.e. compute (1 + 2i/n)(1+2i/n)

Answer 7

give me a sec, i have to write the latex in a document, because i cannot write it here for some reason

Answer 8

this is kind of a pain to write like this, but the first steps are basic algebra
everything without an i in it comes out of the summation
now you can compute the limit one at a time

Answer 9

sum 1 to n of 1 is just n as it is 1+ 1 + 1 + ... + 1 n times
divide it by n and you get 1 for the first sum

Answer 10

last job is to take the limit as n goes to infinity, which is not hard if you think about it correctly

Answer 11

the 1 stays a 1

Answer 12

the second term is a polynomial of degree 2 divided by a polynomial of degree 2
limit is the ratio of the leading coefficients, which is this case is 4 / 2 = 2

Answer 13

third term is a polynomial of degree 3 divided by a polynomial of degree 3, again the limit is the ratio of the leading coefficients

Answer 14

hmm, so from what you've told me, the limit is 2?

Answer 15

@satellite73