Question

Prove that there is no positive integer n such that: 90 < 2^n × (n + 1) < 100

Answer 1

2^7 = 128 > 100, so we're down to n = 1,2,3,4,5,6

we can check each n and show that it's false

Answer 2

2^6 (6 + 1) > 2^6 (2) = 2^7, show 6 doesn't work either

Answer 3

2^5 (5+1) = 2^5 (2 * 3) > 2^6 (3) > 2^6, so 5 doesn't work

Answer 4

Thanks. I didn't know where to start. Discrete math is hell.

Answer 5

yeah, this is one of those proofs that we can easily break up into cases.