Estimating Sums of Alternating Series help

In summary, the conversation discusses the confusion about determining the value of bn+1 and whether it should be equal to, less than, or greater than 0.008. The problem statement specifies that n should be a natural number, which affects the determination of bn+1. The Alternating Series Estimation Theorem can also provide insight into this relationship.
  • #1
Slimsta
190
0

Homework Statement


[PLAIN]http://img696.imageshack.us/img696/3438/46981606.jpg [Broken]


Homework Equations





The Attempt at a Solution


in those squars, I am sure about everything that i did and i get it wrong..
the only thing i don't know is bn+1 how would i know if its =, < or > than 0.008 ?

once i know that, everything else just follow it..
 
Last edited by a moderator:
Physics news on Phys.org
  • #2
someone please?
 
  • #3
i haven't checked your working, but doesn't it ask for n as "an integer"?
 
  • #4
Slimsta said:

The Attempt at a Solution


in those squars, I am sure about everything that i did and i get it wrong..
the only thing i don't know is bn+1 how would i know if its =, < or > than 0.008 ?

once i know that, everything else just follow it..


First, note that n is supposed to be NATURAL NUMBER. So can n have trailing digits after the decimal place? As for whether you should have =, <, or >... reread both the problem statement (the error should be less than .008) as well as the Alternating Series Estimation Theorem (consider the relationship between [itex]b_{n+1}[/itex] and the error).
 

What is an alternating series?

An alternating series is a series in which the signs (+ or -) of the terms alternate. For example, 1 - 2 + 3 - 4 + 5 - ... is an alternating series.

What is the formula for estimating the sum of an alternating series?

The formula for estimating the sum of an alternating series is S = a - b + c - d + ..., where a, b, c, d, ... are the terms of the series. This is known as the Leibniz formula for alternating series.

When can we use the Leibniz formula for estimating sums of alternating series?

The Leibniz formula can be used for alternating series that satisfy the following conditions:
1. The terms of the series decrease in absolute value.
2. The terms of the series approach zero as n approaches infinity.
3. The series has infinitely many terms.

What is the significance of estimating sums of alternating series?

Estimating sums of alternating series is important in mathematics because it allows us to determine the convergence or divergence of a series. This information can be useful in various applications, such as in physics and engineering.

Can the Leibniz formula be used to find the exact sum of an alternating series?

No, the Leibniz formula can only provide an estimate for the sum of an alternating series. To find the exact sum, we would need to use other methods such as finding the limit of the series or using Taylor series.

Similar threads

  • Calculus and Beyond Homework Help
Replies
29
Views
1K
  • Calculus and Beyond Homework Help
Replies
2
Views
2K
  • Calculus and Beyond Homework Help
Replies
1
Views
2K
  • Calculus and Beyond Homework Help
Replies
4
Views
906
  • Calculus and Beyond Homework Help
2
Replies
38
Views
2K
  • Calculus and Beyond Homework Help
Replies
2
Views
786
  • Calculus and Beyond Homework Help
Replies
14
Views
2K
  • Calculus and Beyond Homework Help
Replies
1
Views
810
  • Calculus and Beyond Homework Help
Replies
7
Views
2K
  • Calculus and Beyond Homework Help
Replies
22
Views
3K
Back
Top