List the elements of the setsC = {(n + 1)2 − (n2 + 2n) | n ∈ N}
Question
List the elements of the setsC = {(n + 1)2 − (n2 + 2n) | n ∈ N}
Solution 1
The elements of the set C can be found by simplifying the expression within the set notation.
The expression is (n + 1)² - (n² + 2n).
First, expand (n + 1)² to get n² + 2n + 1.
So, the expression becomes n² + 2n + 1 - n² - 2n.
The n² and 2n terms cancel out, leaving just 1.
Therefore, the set C = {1 | n ∈ N}.
This means that the set C contains only the element 1, regardless of the value of n.
Solution 2
The elements of the set C can be found by simplifying the expression within the set notation.
The expression is (n + 1)² - (n² + 2n).
First, expand (n + 1)² to get n² + 2n + 1.
So the expression becomes n² + 2n + 1 - n² - 2n.
The n² and 2n terms cancel out, leaving just 1.
Therefore, the set C = {1 | n ∈ N}.
This means that the set C contains only the element 1, regardless of the value of n.
Similar Questions
A = {(n + 1)2 − n2 | n ∈ N}is the set of all odd numbers.Write down a similar expression for the set, B, of all even numbers.List the elements of the setsC = {(n + 1)2 − (n2 + 2n) | n ∈ N}and (A ∩ B) ∪ C.
Explain why the setA = {(n + 1)2 − n2 | n ∈ N}is the set of all odd numbers.
Use induction to show that a set with n elements has 2n subsets
Use induction to show that a set with n elements has 2^n subsets.
LetA :=32 − (−1)n2n : n ∈ N.Find inf A and sup A. Justifications are required
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