Partial sums for convergent series

Thread starter kahwawashay1
Start date Dec 11, 2011
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Convergent Partial Series Sums

In summary, partial sums for convergent series are the sum of a finite number of terms in an infinite series. To calculate them, you add up the first n terms of the series, with the partial sum sequence approaching the overall sum of the series as n increases. The main purpose of finding partial sums is to determine whether the series converges or diverges. This concept is related to limits, as the partial sum sequence approaches the limit of the overall sum. However, partial sums cannot be used to find the exact sum of a divergent series, as other methods may need to be used.

Dec 11, 2011

kahwawashay1

Is it possible to find a non-recursive formula for the partial sums of a convergent series?

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Dec 11, 2011

kahwawashay1

kahwawashay1 said:

Is it possible to find a non-recursive formula for the partial sums of a convergent series?

nvm, i found one

Related to Partial sums for convergent series

1. What is the definition of partial sums for convergent series?

Partial sums for convergent series refer to the sum of a finite number of terms in an infinite series. It is used to determine the overall sum of the series, which may not be possible to calculate using traditional methods.

2. How do you calculate partial sums for convergent series?

To calculate partial sums for convergent series, you need to add up the first n terms of the series. As n increases, the partial sums will approach the overall sum of the series. This is known as the partial sum sequence.

3. What is the purpose of finding partial sums for convergent series?

The main purpose of finding partial sums for convergent series is to determine whether the series converges or diverges. If the partial sum sequence approaches a finite value, then the series is said to converge. If the partial sum sequence approaches infinity, then the series is said to diverge.

4. How does the concept of partial sums relate to the concept of limits?

The concept of partial sums is closely related to the concept of limits. As the number of terms in the partial sum sequence increases, it approaches the limit of the overall sum of the series. This is similar to how the limit of a function is determined by looking at the values of the function as the input approaches a certain value.

5. Can partial sums be used to find the exact sum of a divergent series?

No, partial sums can only be used to determine the overall sum of a convergent series. If a series is divergent, meaning the partial sum sequence approaches infinity, then it is not possible to find the exact sum using this method. Other methods, such as the geometric series formula, may need to be used to find the sum of a divergent series.