输血181讨论稿质疑，请进

擎天柱

181: DS: 假设有一个数列S(n),已知S(0), 求S(n),

1) S(i) is i more than s(i-1) for any i>=1

2) the difference between S(i) and S(i-1) is i^2

条件一 可求S(i)=s(i-1)+i

条件二 可求S(i)=s(i-1)+i^2选D

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我觉得这道题目选A
条件2是不确定的，题目中的意思是|S(i) - S(i-1)|=i^2
这样就是求出的S(i)会有正负两个数值不能确定哦~~~
大家怎么看？

BeBrave2011

|S(i) - S(i-1)|=i^2 不是difference，是distance。

擎天柱

感谢LS的~~~请问difference代表啥？是去掉绝对值的吗？好诡异啊~~~

擎天柱

|S(i) - S(i-1)|=i^2 不是difference，是distance。

-- by 会员 BeBrave2011 (2010/10/30 6:39:21)

感谢LS的~~~请问difference代表啥？是去掉绝对值的吗？好诡异啊~~~

BeBrave2011

这个确实是个有争议的问题。不过我觉得没有必要想的太复杂，你看下面的解释。

Date: 09/22/2006 at 23:11:55
From: Doctor Peterson
Subject: Re: What is the difference between 8 and 5? or between 5 and 8?

Hi, Mary.

Elementary algebra books tend to twist the English language a bit
here, to make things easier for the students.  In real life, the
difference between a and b is |a-b| (or |b-a|, which is the same);
differences are always positive.  But that would lead to ugly
equations that students would struggle to solve; so they pretend that
when we say "the difference of a and b" we mean just a-b--in that
order, even though if b were greater than a, the "difference" would be
negative.

(In fact, there are some cases in math where we _would_ allow a
negative difference; the one that comes to mind is when we take
"successive differences" in a sequence to see how it is made, and
consider the difference from one term to the next to be the second
minus the first, regardless of which is greater.  But we wouldn't
quite use the same phrase as in the textbooks!)

Anyway, regardless of the usual rules in real life, for the sake of
problems in this course, your "thoughts" represent what they want you
to do.

Here's a similar question from our archives that you might find
interesting as it discusses the use of absolute value in these situations:

 The Difference of x and y...
   http://mathforum.org/library/drmath/view/63137.html

If you have any further questions, feel free to write back.


- Doctor Peterson, The Math Forum
 http://mathforum.org/dr.math/