The following formula is used to calculate the sum of a convergent series:
\[ S = \frac{a}{1 - r} \]
Where:
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.
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.
Let's say you have a series with a first term of 5 and a common ratio of 0.5. Using the formula:
\[ S = \frac{5}{1 - 0.5} = \frac{5}{0.5} = 10 \]
So, the sum of the series is 10.
