Sure, let's break it down:

1. First, let's simplify the expression (n + 1)² - n². This can be expanded to n² + 2n + 1 - n². The n² terms cancel out, leaving us with 2n + 1.

2. The expression 2n + 1 is the general form for all odd numbers. This is because any number multiplied by 2 gives an even number, and adding 1 to an even number results in an odd number.

3. Therefore, the set A = {(n + 1)² - n² | n ∈ N} represents all odd numbers, because for each natural number n, the expression (n + 1)² - n² simplifies to an odd number.

Question

Sure, let's break it down:

1. First, let's simplify the expression (n + 1)² - n². This can be expanded to n² + 2n + 1 - n². The n² terms cancel out, leaving us with 2n + 1.

2. The expression 2n + 1 is the general form for all odd numbers. This is because any number multiplied by 2 gives an even number, and adding 1 to an even number results in an odd number.

3. Therefore, the set A = {(n + 1)² - n² | n ∈ N} represents all odd numbers, because for each natural number n, the expression (n + 1)² - n² simplifies to an odd number.

Knowee AI · Accepted Answer

Sure, let's break it down:

1. First, let's simplify the expression (n + 1)² - n². This can be expanded to n² + 2n + 1 - n². The n² terms cancel out, leaving us with 2n + 1.

2. The expression 2n + 1 is the general form for all odd numbers. This is because any number multiplied by 2 gives an even number, and adding 1 to an even number results in an odd number.

3. Therefore, the set A = {(n + 1)² - n² | n ∈ N} represents all odd numbers, because for each natural number n, the expression (n + 1)² - n² simplifies to an odd number.

Explain why the setA = {(n + 1)2 − n2 | n ∈ N}is the set of all odd numbers.

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