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AJW99
 2 years ago
Best ResponseYou've already chosen the best response.0Express the following in closed form \[\sum_{k=1}^{n}(2+2*\frac{ k }{ n })^2\]

uber1337h4xx0r
 2 years ago
Best ResponseYou've already chosen the best response.0Lemme double check what exactly closed form is and I may be able to assist.

uber1337h4xx0r
 2 years ago
Best ResponseYou've already chosen the best response.0Dang it... it appears as though closed form deals with diff eq (according to a quick google). I am only at Cal 2, so I think I'm going to have to sit this one out :/

satellite73
 2 years ago
Best ResponseYou've already chosen the best response.1\[\sum_{k=1}^{n}(2+\frac{2 k }{ n })^2\]?

satellite73
 2 years ago
Best ResponseYou've already chosen the best response.1gotta square it first

satellite73
 2 years ago
Best ResponseYou've already chosen the best response.1oh no, square the whole thing

satellite73
 2 years ago
Best ResponseYou've already chosen the best response.1\[(2+\frac{2k}{n})(2+\frac{2k}{n})=4+\frac{8k}{n}+\frac{4k^2}{n^2}\]

Mr.Me
 2 years ago
Best ResponseYou've already chosen the best response.0then distribute the summation

satellite73
 2 years ago
Best ResponseYou've already chosen the best response.1now break it up in to three summations \[\sum_{k=1}^n4=4n\] is the first one

satellite73
 2 years ago
Best ResponseYou've already chosen the best response.1\[\sum_{k=1}^n\frac{8k}{n}=\frac{8}{n}\sum_{k=1}^nk\] for the second do you know how to add \[\sum_{k=1}^nk\]?

satellite73
 2 years ago
Best ResponseYou've already chosen the best response.1notice that \(n\) is fixed so it comes out of the summation

AJW99
 2 years ago
Best ResponseYou've already chosen the best response.0I am really lost on how to do sigmas. I really appreciate the help you are giving me

Mr.Me
 2 years ago
Best ResponseYou've already chosen the best response.0\[\frac{4 n(n+1)(2n+1) }{ 6n ^{2} }\]

satellite73
 2 years ago
Best ResponseYou've already chosen the best response.1the formula for \[\sum_{k=1}^nk=1+2+3+...+n=\frac{n(n+1)}{2}\]

satellite73
 2 years ago
Best ResponseYou've already chosen the best response.1so the second term gives \[\frac{8}{n}\sum_{k=1}^nk=\frac{8}{n}\frac{n(n+1)}{2}=4(n+1)\]

satellite73
 2 years ago
Best ResponseYou've already chosen the best response.1the last one is \[\sum_{k=1}^n\frac{4k^2}{n^2}\] and as in the previous case the \(\frac{4}{n^2}\) comes out front to give you \[\frac{8}{n^2}\sum_{k=1}^nk^2\] so what you need for this one is the formula for \[\sum_{k=1}^nk^2\] which i am going to guess you do not know, but it is probably in your book

satellite73
 2 years ago
Best ResponseYou've already chosen the best response.1http://polysum.tripod.com/ yes it is!

satellite73
 2 years ago
Best ResponseYou've already chosen the best response.1so you get for the last term \[\frac{4}{n^2}\frac{n(n+1)(2n+1)}{6}\] oops you were off by a little

satellite73
 2 years ago
Best ResponseYou've already chosen the best response.1should be \(2n+1\) in the numerator, not \(n+2\)

satellite73
 2 years ago
Best ResponseYou've already chosen the best response.1it is algebra from here on in

satellite73
 2 years ago
Best ResponseYou've already chosen the best response.1but one answer is \[4n+4n+1+\frac{4}{n^2}\frac{n(n+1)(2n+1)}{6}\]

satellite73
 2 years ago
Best ResponseYou've already chosen the best response.1unless of course i messed up my algebra let me check

satellite73
 2 years ago
Best ResponseYou've already chosen the best response.1i am off somewhere not sure exactly where

satellite73
 2 years ago
Best ResponseYou've already chosen the best response.1oh damn distributive law!! \(4(n+1)=4n+4\)!!

satellite73
 2 years ago
Best ResponseYou've already chosen the best response.1\[4n+4n+4+\frac{4}{n^2}\frac{n(n+1)(2n+1)}{6}\]

AJW99
 2 years ago
Best ResponseYou've already chosen the best response.0I see now . Thank you so much for your help I really appreciate it!

satellite73
 2 years ago
Best ResponseYou've already chosen the best response.1here we can check what it looks like in a nice form

satellite73
 2 years ago
Best ResponseYou've already chosen the best response.1http://www.wolframalpha.com/input/?i=4n%2B4n%2B4%2B\frac{4}{n^2}\frac{n%28n%2B1%29%282n%2B1%29}{6} so one way to write this mess is \[\frac{2(2n+1)(7n+1)}{3n}\]

satellite73
 2 years ago
Best ResponseYou've already chosen the best response.1and we can also check that it is in fact correct http://www.wolframalpha.com/input/?i=\sum_{k%3D1}^{n}%282%2B\frac{2+k+}{+n+}%29^2

satellite73
 2 years ago
Best ResponseYou've already chosen the best response.1copy and paste, you will see it , and see that it is right
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