(Choose 1 answer)
(See picture)
A. 1, 2, 3, 4, 5
B. 3, 2, 4, 1, 5
C. 3, 4, 2, 1,5
D. 1, 3, 2, 5, 4
E. None of the other choices is correct
Find the correct order of steps of a proof by induction method
for the problem:
"Prove that for all positive integers n we have n^{3}+2n is divisible by 3".
1. Indeed, (k+1)3+2(k+1)=(k³+2k)+3(k2+3k+1) is divisible by 3 by inductive hypothesis.
2. Assume k^{3}+2k is divisible by 3 for some positive integer k.
3. If n=1 then 1^{3}+2(1)=3 is divisible by 3.
4. We need to show that (k+1)^{3}+2(k+1) is divisible by 3.
5. Therefore, n^{3}+2n is divisible by 3 for all positive integer n.
Exit 21
