Final answer:
Sigma notation is a way to represent the sum of a series of numbers. It is used in mathematics to express arithmetic, geometric, harmonic, and convergent series. By writing the series in terms of sigma notation, it becomes easier to work with and analyze various types of sequences and series.
Step-by-step explanation:
Sigma notation, also known as summation notation, is a way to represent the sum of a series of numbers. It is commonly used in mathematics to express arithmetic, geometric, harmonic, and convergent series. To use sigma notation, you write the series as the sum of terms, with an index variable specifying the starting and ending values of the series.
For example, for an arithmetic series, the sigma notation would be written as Σ(k=1 to n) a + (k-1)d, where a is the first term, d is the common difference, and n is the number of terms in the series. Similarly, for a geometric series, the sigma notation would be written as Σ(k=1 to n) ar^(k-1), where a is the first term, r is the common ratio, and n is the number of terms.
Using sigma notation can simplify the representation and calculation of series, making it easier to work with and analyze various types of sequences and series.
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