1 Answer | Add Yours
We can prove that 2^n > n for all positive integers n by induction.
First for n = 1, 2^n = 2 which is greater than 1.
Assume 2^n > n
Now 2^(n + 1) should be greater than (n + 1)
2^(n + 1) = 2*2^n > 2n
2n = n + n > n + 1
=> 2^(n + 1) > n + 1 if 2^n > n
This proves that 2^n > n for all positive integers n.
We’ve answered 318,974 questions. We can answer yours, too.Ask a question