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General Reimann sum questions

  • #1
I have a homework question which asks about Reimann sums (which I feel relatively comfortable with), but I just don't know what they're asking. Here's the image

https://dl.dropbox.com/u/38457740/maff.bmp [Broken]
 
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Answers and Replies

  • #2
294
0
For the second one there, what is the sum of all numbers between 1 and n?
 
  • #3
Thanks for the reply. Found out I'm not following at least a couple rules to the forum, but it wouldn't let me delete my post. :/

40, obviously, is my attempt at problem one, but that was with the help of a teacher (not sure if it's correct yet..)

To answer your question, wouldn't that just be the given part of the problem, condensed to (n^2-n)/2?
 
  • #4
294
0
To answer your question, wouldn't that just be the given part of the problem, condensed to (n^2-n)/2?
Close, but not quite the right formula. The condensed form that they gave is ##\frac{n^2 + n}{2}##, is that what you meant?
 
  • #5
Whoops, yeah I switched the sign.

Part of what's confusing me is the j=41 under each sigma, where I'm used to seeing 0 or 1. When the function is j or j^2, etc, does this mean that the start point is 41 and 41^2, respectively?

I'm not sure if this even helps me solve the problem, but I'm trying to get a grip on what every variable means here.
 
  • #6
Bacle2
Science Advisor
1,089
10
I think the main idea is : Sum from 1 to n -(sum from 41 to n )= ....
 
  • #7
294
0
Whoops, yeah I switched the sign.

Part of what's confusing me is the j=41 under each sigma, where I'm used to seeing 0 or 1. When the function is j or j^2, etc, does this mean that the start point is 41 and 41^2, respectively?

I'm not sure if this even helps me solve the problem, but I'm trying to get a grip on what every variable means here.
These do start with 41 and 41^2 instead of 1 and 1^2, but the formula they have (the ##\frac{x(x+1)}{2}##) is for the sequence that starts with 1.

So that means that you can rewrite the formula given as a sigma notation from 1 to n and then simplify from there.
 

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