Here are the essential concepts you must grasp in order to answer the question correctly.
Odd Integers
Odd integers are numbers that are not divisible by 2, typically represented in the form of 2n - 1, where n is a positive integer. The sequence of the first n positive odd integers starts from 1 and continues as 1, 3, 5, ..., up to (2n - 1). Understanding this sequence is crucial for analyzing their sum.
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Summation of Series
The summation of a series involves adding a sequence of numbers together. In this case, we are summing the first n odd integers. Recognizing the pattern in the series helps in deriving a formula for the sum, which in this case is shown to equal n².
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Mathematical Induction
Mathematical induction is a proof technique used to establish the truth of an infinite number of statements. It involves two steps: proving the base case and then showing that if the statement holds for n, it also holds for n + 1. This method can be applied to prove that the sum of the first n odd integers equals n².
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