Kizspy | Question: 20
(Choose 1 answer)
(See picture)
A. (i)
B. (ii)
C. (iii)
D. None of the other choices
FUOVERFLOW
Let P(n) be the statement "f(n) is even", where f(n)=n2+7n+3.The domain consists of all positive integers.
A proof ofVnP(n) is as follows:
(i) P(1) is clearly true.
(ii) Assume that P(k) is true for some positive integer k,which means that f(k) is even.
(iii) We have:f(k+1)= (k+1)2+7(k+1)+3=(k²+7k+3)+(2k+8)= f(k)+2(k+4)is even, since it is written as a sum of two even integers. Thus P(k+1) is true. By induction, we conclude VnP(n).
Which step is wrong in this proof?
