Question

Write the set { 1, 3, 7, 15, 31, 63 } in set builder form ​

Answer 1

Answer:

{ x : x = 2^n -1 , n ∈ N}

Where N is the set of natural numbers

Step-by-step explanation:

Mathematically, we can rewrite each term in the set as follows;

1 = 2^1 - 1

3 = 2^2 -1

7 = 2^3 -1

15 = 2^4-1

31 = 2^5-1

63 = 2^6 -1

so we can conclude that the nth term is 2^n -1

So writing this in set builder notation, we have;

{ x : x = 2^n -1 , n ∈ N}

Where N is the set of natural numbers