General Reimann sum questions

[veegeedeejay]

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]

 

[Villyer]

For the second one there, what is the sum of all numbers between 1 and n?

 

[veegeedeejay]

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?

 

[Villyer]

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?

 

[veegeedeejay]

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.

 

[Bacle2]

I think the main idea is : Sum from 1 to n -(sum from 41 to n )= ....

 

[Villyer]

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.