Kizspy Question: 25
(Choose 1 answer)
(See picture)
A. 1, 2, 4, 3
B. None of the other choices is correct
C. 1, 2, 3, 4
D. 2, 1, 3, 4
E. 2, 1, 4, 3
Find the correct order of steps of a proof by induction of the problem
"Prove that for all positive integers n > 6 then 3" <n!"
1. Assume the inequality is true for some k> 6. We need to
show that 3k+1 < (k+1)!.
2. Forn 7 then 37 = 72187<7! = 5040.
3. Then 3n<n! for all positive integers n > 6.
4. Indeed, 3k+1=3.3k <3(k!) by the induction hypothesis. Since
3(k!) (k+1)! for k> 6, we have 3k+1 < (k+1)!.
