(Choose 1 answer)
(See picture)
A. (ii)
B. (i)
C. (iii)
D. None of the other choices
Let P(n) be the statement "f(n) is odd", where f(n)=n²+9n+2.The domain consists of all positive integers.
A proof ofVnP(n) is as follows:
P(1) is clearly true.
(ii) Assume that P(k) is true for some positive integer k,which means that f(k) is odd.
(iii) We have:f(k+1)= (k+1)2+9(k+1)+2=(k²+9k+2)+(2k+10)= f(k)+2(k+5)
is odd, as it is a sum of an odd integer and an even integer. Thus P(k+1) is true. By induction, we conclude VnP(n).
Which step is wrong in this proof?
Exit 47
