Write the set A = \{1, 4, 9, 16, 25, . . . \} in set-builder form.
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Step-by-Step Solution
Step 1: Identify the pattern
Observe the elements of the given set A. We can see that each element is the square of a natural number. The first element is 12, the second is 22, the third is 32, and so on.
Step 2: Define the general term
Based on the observed pattern, we can represent any element x in the set as the square of a natural number n. Here, n belongs to the set of natural numbers, denoted by N={1,2,3,...}.
Step 3: Write in set-builder form
Using the general term, we can write the set A in set-builder form. This notation means 'the set of all x such that x is equal to n2, where n is a natural number'.