如何找到总和的增长顺序？
[英]How to find the order of growth of a sum?
问题描述
I am wondering how to find the order of growth of: the sum from 0 to n-1 of (i^2+1)^2 
我想知道如何找到(i^2+1)^2从0到n-1的和的增长顺序
First of all, I am assuming that I need to just find the closed-form of the summation (ie just as the sum from 1 to n of k is (n(n+1))/2 ). 首先，我假设我只需要找到求和的闭合形式（即，就像从k的1到n的总和是(n(n+1))/2 。
Assuming this is true, how do I tackle this problem? 假设这是真的，我该如何解决这个问题？ I have never worked to find the closed-form of a summation where the terms to be summed are of such a high order of magnitude (the 4th power). 我从未尝试过找到求和项的闭合形式，其中要求和的项具有如此高的数量级（四次方）。
Yes, this is a homework problem, but the teacher didn't explain it at all and it doesn't look like anyone has discussed a problem of this type on SO. 是的，这是一个家庭作业问题，但老师根本没有解释，似乎没有人在SO上讨论过此类问题。 Any help I can get would really be appreciated. 我能得到的任何帮助将不胜感激。
1 个解决方案
解决方案1
1 2015-02-03 09:24:50
I am not going to finish your homework, but provide you with some hints. 我不会完成您的作业，但会为您提供一些提示。
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(a+b)^2 = a^2 + b^2 + 2ab - summation of
a^ican be found from wikipedia page http://en.wikipedia.org/wiki/Summation可从Wikipedia页面http://en.wikipedia.org/wiki/Summation中找到a^i总和。
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