Calculus 2, Series Convergence Questions?

In summary, the conversation discusses problems with series and convergence. The speaker shares their attempts at solving the problems and mentions using the ratio test, but expresses difficulty in understanding and completing the problems by the deadline. They also mention having trouble with alternating series and reveal that they had one problem marked wrong, but did not specify which one. The conversation ends with a question about the absolute convergence of a particular problem and a realization that the third problem was incorrect.
  • #1
MMhawk607
5
0
I have some problems here with Series and Convergence...

Here are the problems and my guesses at it.

http://img822.imageshack.us/img822/9523/23341530.png

It won't tell me which one is wrong, but it just says one/all is wrong. Any help is appreciated.

Attempts at solving, I tried using ratio test for these but I can't seem to get it. I need more comprehension of these types of problems I know, but these problems are due by tonight.
Alternating series really give me trouble too.
 
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  • #2
OH

It was because of the third problem

sin(3n)/n^2

Is it because

sin(3n) / (n^2) ≤ 1/(n^2)

Therefore the p test makes it absolutely convergent?

I had the other 4 right, I figured that one was A though, is this the reason?
 
  • #3
MMhawk607 said:
OH

It was because of the third problem

sin(3n)/n^2

Is it because

sin(3n) / (n^2) ≤ 1/(n^2)

Therefore the p test makes it absolutely convergent?

I had the other 4 right, I figured that one was A though, is this the reason?
Hello MMhawk607. Welcome to PF !

Yes, you had #3 wrong .

It is absolutely convergent.
 
  • #4
mmhawk607 said:
i have some problems here with series and convergence...

Here are the problems and my guesses at it.

http://img822.imageshack.us/img822/9523/23341530.png

it won't tell me which one is wrong, but it just says one/all is wrong. Any help is appreciated.

Attempts at solving, i tried using ratio test for these but i can't seem to get it. I need more comprehension of these types of problems i know, but these problems are due by tonight.
Alternating series really give me trouble too.
...                         .
 
Last edited by a moderator:

FAQ: Calculus 2, Series Convergence Questions?

1. What is the definition of a convergent series in Calculus 2?

A convergent series in Calculus 2 is defined as a series whose terms approach a finite limit as the number of terms increases. In other words, as the number of terms in the series gets larger and larger, the sum of those terms approaches a specific value.

2. How do you determine if a series is convergent or divergent?

To determine if a series is convergent or divergent, you can use several tests such as the comparison test, ratio test, or root test. These tests involve analyzing the behavior of the terms in the series and comparing it to a known convergent or divergent series.

3. What is the difference between absolute and conditional convergence?

Absolute convergence refers to a series where the sum of the absolute values of the terms converges, while conditional convergence refers to a series where the sum of the terms converges, but not the absolute values. In other words, conditional convergence implies absolute convergence, but not vice versa.

4. Can a series have both positive and negative terms and still be convergent?

Yes, a series can have both positive and negative terms and still be convergent. For example, the alternating series (-1)^n/n^2 oscillates between positive and negative terms, but it is still convergent as the terms approach zero as n approaches infinity.

5. How can you use the integral test to determine the convergence of a series?

The integral test states that if the function f(x) is continuous, positive, and decreasing for all values greater than or equal to n, then the series ∑f(n) is convergent if and only if the integral ∫f(x)dx from n to infinity is also convergent. This means that if the integral diverges, then the series also diverges, and if the integral converges, then the series also converges.

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