Finding Sum of Alternating Series to Desired Accuracy

In summary, an alternating series is a series where the terms alternate in sign, and the sum of an alternating series is the value that the series converges to. To find the sum, one can use the alternating series test, where the terms decrease in absolute value and approach 0. The sum can be negative due to the alternating signs of the terms. The desired accuracy for finding the sum refers to the level of precision desired, which can be specified in terms of decimal places or percentage of error.
  • #1
lindsaygilber
3
0
How many terms of the series do we need to add in order to find the sum to the indicated accuracy?

The alternating series from n=1 to infinity of ((-1)^(n+1))/(n^2)
|error| less than 0.0399
i got it down to 1/n^2 is less than 0.0399 but i can't figure out if n = 5 or n=6... please help:(
 
Last edited:
Physics news on Phys.org
  • #2
If you want 1/n2< 0.0399, then you want 1/0.0399= 25.0626< n2 While it is close hat is NOT true for n= 5.
 

Related to Finding Sum of Alternating Series to Desired Accuracy

What is an alternating series?

An alternating series is a series where the terms alternate in sign. For example, the series 1 - 2 + 3 - 4 + 5 - ... is an alternating series.

What is the sum of an alternating series?

The sum of an alternating series is the value that the series converges to, if it converges. In other words, it is the value that the series approaches as more terms are added.

How do you find the sum of an alternating series?

To find the sum of an alternating series, you can use a process called the alternating series test. This test states that if the terms of the series decrease in absolute value and approach 0, then the series will converge to a specific value. This value can be found by summing the terms until the desired accuracy is reached.

Can the sum of an alternating series be negative?

Yes, the sum of an alternating series can be negative. This is because the terms of the series can alternate between positive and negative values, resulting in a negative sum.

What is the desired accuracy for finding the sum of an alternating series?

The desired accuracy for finding the sum of an alternating series refers to the level of precision that is desired for the sum. This can be a specific number of decimal places or a percentage of error. It is important to specify the desired accuracy in order to accurately calculate the sum of the series.

Similar threads

How to show that these sequences are summable?
    • Calculus and Beyond Homework Help
Replies
1
Views
429
Does the Alternating Series Test show convergence for this series?
    • Calculus and Beyond Homework Help
Replies
14
Views
1K
Fourier series of this scale and shift of triangle wave
    • Calculus and Beyond Homework Help
Replies
1
Views
315
Learning to use the Cauchy criterion for infinite series
    • Calculus and Beyond Homework Help
Replies
7
Views
1K
POTW Sum of an Alternating Series
    • Math POTW for University Students
Replies
16
Views
841
Multiplication of Taylor and Laurent series
    • Calculus and Beyond Homework Help
Replies
12
Views
2K
Understanding the Ratio Test for Series and Its Applications
    • Calculus and Beyond Homework Help
Replies
7
Views
1K
Finding the Limit of a Series: Exploring Different Patterns and Approaches
    • Calculus and Beyond Homework Help
Replies
2
Views
892
Finding 2 solutions of this Bessel's function using a power series
    • Calculus and Beyond Homework Help
Replies
8
Views
1K
Studying the convergence of a series with an arctangent of a partial sum
    • Calculus and Beyond Homework Help
Replies
7
Views
1K

Hot Threads

Recent Insights

Back
Top