Understanding Reimann Sums: Interpreting Variables and Formulas

  • Thread starter Thread starter veegeedeejay
  • Start date Start date
  • Tags Tags
    General Sum
Click For Summary
SUMMARY

This discussion focuses on understanding Riemann sums, specifically in the context of summing integers from 1 to n and interpreting variables in sigma notation. The correct formula for the sum of the first n integers is established as (n^2 + n)/2. Participants clarify the significance of starting points in sigma notation, noting that the variable j can start at 41 instead of the typical 0 or 1, which affects the interpretation of the sums. The conversation emphasizes the need to rewrite formulas in sigma notation for clarity and accuracy.

PREREQUISITES
  • Understanding of Riemann sums
  • Familiarity with sigma notation
  • Basic algebraic manipulation skills
  • Knowledge of arithmetic series formulas
NEXT STEPS
  • Study the derivation of the formula for the sum of the first n integers: (n^2 + n)/2
  • Learn how to convert arithmetic series into sigma notation
  • Explore the implications of changing the starting index in sigma notation
  • Practice problems involving Riemann sums and their applications in calculus
USEFUL FOR

Students studying calculus, mathematics educators, and anyone looking to deepen their understanding of Riemann sums and sigma notation.

veegeedeejay
Messages
3
Reaction score
0
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
 
Last edited by a moderator:
Physics news on Phys.org
For the second one there, what is the sum of all numbers between 1 and n?
 
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?
 
veegeedeejay said:
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?
 
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.
 
I think the main idea is : Sum from 1 to n -(sum from 41 to n )= ...
 
veegeedeejay said:
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.
 

Similar threads

Using Euler's formula to prove trig identities using "sum to product" technique
  • · Replies 4 ·
Replies
4
Views
2K
Integral of x^n using Reimann sums
  • · Replies 4 ·
Replies
4
Views
1K
Determine marginal densities and distributions from joint density
  • · Replies 7 ·
Replies
7
Views
1K
Help me understand why this summation index is not j
  • · Replies 11 ·
Replies
11
Views
1K
Find the limit of the sum of the areas of all these triangles
  • · Replies 7 ·
Replies
7
Views
1K
Is My Reimann Sum Solution Correct for 6/(1+2x) from 0 to 2 with 4 Subintervals?
  • · Replies 3 ·
Replies
3
Views
2K
Finding the least possible sum of a product.
  • · Replies 3 ·
Replies
3
Views
4K
Finding an explicit formula for the sequence of partial sums
  • · Replies 2 ·
Replies
2
Views
5K
Formulas for Sequences: Finding Limits and Sums for an, Sn, and Rn
  • · Replies 3 ·
Replies
3
Views
3K
Solve (t^2-1)y'' +4ty'+2y=6t, given two particular solutions
  • · Replies 2 ·
Replies
2
Views
1K