Sum Series Explicit Formula

In summary, the conversation discusses finding an explicit formula for the sum of a series, with the given formula for any term in the series being 1/(2n(n+3)). The suggestion to use partial fractions is brought up and it is mentioned that this method can be successful in finding the sum. The conversation concludes with expressions of appreciation for the helpful solution.
  • #1
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Homework Statement



Find an explicit formula for the sum of the series, given that the formula for any term in the series is [tex]\frac{1}{2n(n+3)}[/tex]

Homework Equations





The Attempt at a Solution

 
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  • #2
Try splitting it into partial fractions and see if that takes you anywhere.
 
  • #3
rock.freak667 said:
Try splitting it into partial fractions and see if that takes you anywhere.

That'll diverge, won't it? :confused:
 
  • #4
tiny-tim said:
That'll diverge, won't it? :confused:

It's similar to 1/n^2. That's a p series with p=2. It converges.
 
  • #5
tiny-tim said:
That'll diverge, won't it? :confused:
I'm not sure what you mean by that, since you said this, not in response to the initial post, but in response to the suggestion to use partial fractions to split it into to parts.

Perhaps you meant that the two parts would each diverge separately. But that's not the point- you don't want to look at them separately- you want to see if there are terms at one point that will cancel terms at another point. In fact, partial fractions works nicely.
 
  • #6
HallsofIvy said:
… Perhaps you meant that the two parts would each diverge separately. But that's not the point- you don't want to look at them separately- you want to see if there are terms at one point that will cancel terms at another point. In fact, partial fractions works nicely.

oh yes … so it does … isn't that nice!

thanks, HallsofIvy! :smile:
 

What is a sum series explicit formula?

A sum series explicit formula is a mathematical formula that allows you to find the sum of a series of numbers by plugging in the first and last terms of the series, as well as the number of terms in the series.

How do you derive a sum series explicit formula?

To derive a sum series explicit formula, you can use the formula for the sum of an arithmetic series or the sum of a geometric series, depending on the type of series you are working with. You can also use algebraic manipulation to find a general formula for the sum of any series.

What is the difference between a sum series explicit formula and a recursive formula?

A sum series explicit formula is a direct formula that allows you to find the sum of a series without having to calculate each individual term. A recursive formula, on the other hand, requires you to know the previous term in order to find the next term, making it more time-consuming for finding the sum of a series.

Can a sum series explicit formula be used for infinite series?

No, a sum series explicit formula can only be used for finite series, meaning a series with a specific number of terms. For infinite series, other methods such as limits or convergence tests must be used to find the sum.

What is the purpose of using a sum series explicit formula?

The purpose of using a sum series explicit formula is to quickly and accurately find the sum of a series without having to calculate each individual term. This can save time and effort in solving mathematical problems that involve series and can also provide a more general solution for any series of the same type.

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