Principle Of Mathematical Induction Question 4

Question: If $ p(n)=n^{2}+n, $ $ \forall ,n\in N $ , then p(n) is

Options:

A) even positive integer

B) prime number

C) odd integer

D) multiple of 4

Show Answer

Answer:

Correct Answer: A

Solution:

  • [a] $ P(n)=n^{2}+n: $
    $ P(1)=1+1=2; $
    $ P(2)=2^{2}+2=6; $
    $ P(3)=3^{2}+3=12 $
    We observe that $ \forall n\in N, $ $ P(n) $ is always an even positive integer.