Series - convergent or divergent?

In summary, the conversation is discussing a series and determining whether it is convergent or divergent. The first person is also seeking help in finding the sum of the series.
  • #1
knv
17
0
Series -- convergent or divergent?

1. Determine whether the following series is convergent or divergent. When a series is convergent, find the sum. If it diverges, find if it is infinity, - inf, or DNE.

Ʃ [(1/na) - 1/ (n+1)a]




2. we are finding if a >0



3. I know that it converges but I do not know how to find the sum of it. Can anyone help me? At least get me going in the right direction
 
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  • #2


why don't you try redefining the summation variable in ONE of the two terms ...
what would a wise choice be?
 
  • #3
hi knv! :smile:
knv said:
I know that it converges but I do not know how to find the sum of it.

try writing out the sum of the first three or four terms …

do you see a pattern? :wink:​
 

Related to Series - convergent or divergent?

1. What is a convergent series?

A convergent series is a mathematical series in which the sequence of partial sums approaches a finite limit as the number of terms increases.

2. How can you tell if a series is convergent or divergent?

One way to determine if a series is convergent or divergent is by using the ratio test, which compares the terms in the series to the terms in a geometric series. If the ratio between consecutive terms is less than 1, the series is convergent. If the ratio is greater than 1, the series is divergent.

3. What is a divergent series?

A divergent series is a mathematical series in which the sequence of partial sums does not approach a finite limit as the number of terms increases. This means that the sum of the terms in the series becomes infinitely large.

4. What is the significance of convergent and divergent series?

Convergent and divergent series are important in mathematics because they help us understand the behavior of infinite sequences of numbers. They are used in various applications, such as in calculus and statistics, to analyze and solve problems.

5. Can a series be both convergent and divergent?

No, a series cannot be both convergent and divergent. A series can only have one of these two properties. If a series is neither convergent nor divergent, it is said to be oscillating or indeterminate.

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