Enter the first term and the common ratio into the calculator to determine the sum of the series. This calculator can also evaluate any of the variables given the others are known.
Summation Convergence Formula
The following formula is used to calculate the sum of a convergent series.
S = a / (1 - r)
Variables:
- S is the sum of the series
- a is the first term of the series
- r is the common ratio of the series
To calculate the sum of a convergent series, divide the first term of the series by the difference between 1 and the common ratio of the series.
What is a Summation Convergence?
Summation convergence refers to the concept in mathematics where a series or sequence of numbers has a finite sum. This means that as you continue to add more terms to the series, the total does not go towards infinity but instead approaches a specific number. This specific number is known as the sum of the series. If a series does not have a finite sum, it is said to be divergent. The study of summation convergence is a fundamental aspect of calculus and analysis.
How to Calculate Summation Convergence?
The following steps outline how to calculate the Summation Convergence.
- First, determine the first term of the series (a).
- Next, determine the common ratio of the series (r).
- Next, gather the formula from above = S = a / (1 – r).
- Finally, calculate the Summation Convergence.
- After inserting the variables and calculating the result, check your answer with the calculator above.
Example Problem :
Use the following variables as an example problem to test your knowledge.
first term of the series (a) = 3
common ratio of the series (r) = 0.5
