Here are the essential concepts you must grasp in order to answer the question correctly.
Summation Notation
Summation notation is a mathematical shorthand used to represent the sum of a sequence of numbers. It typically uses the Greek letter sigma (Σ) to denote the sum, with an index of summation that indicates the starting and ending values. For example, Σ from i=1 to n represents the sum of all integers from 1 to n.
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Index of Summation
The index of summation is a variable that represents the position of each term in the sequence being summed. In the expression Σ from i=1 to n, 'i' is the index that takes on integer values starting from 1 up to n. This index allows us to systematically add each term in the sequence, making it easier to express and compute sums.
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Arithmetic Series
An arithmetic series is the sum of the terms of an arithmetic sequence, where each term increases by a constant difference. The sum of the first n natural numbers, such as 1 + 2 + 3 + ... + 30, can be calculated using the formula S_n = n/2 * (first term + last term). Understanding this concept helps in efficiently calculating sums without listing all terms.
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