Given:
P(n) = n2 – n + 41 is prime.
P(n) = n2 – n + 41
P (1) = 1 – 1 + 41
= 41
P (1) is Prime.
Similarly,
P(2) = 22 – 2 + 41
= 4 – 2 + 41
= 43
P (2) is prime.
Similarly,
P (3) = 32 – 3 + 41
= 9 – 3 + 41
= 47
P (3) is prime
Now,
P (41) = (41)2 – 41 + 41
= 1681
P (41) is not prime
Hence, P (1), P(2), P (3) are true but P (41) is not true.
Answered by Aaryan | 1 year agoGiven an example of a statement P (n) such that it is true for all n ϵ N.
a + (a + d) + (a + 2d) + … + (a + (n-1)d) = \( \dfrac{n}{2}\) [2a + (n-1)d]
72n + 23n – 3. 3n – 1 is divisible by 25 for all n ϵ N
n (n + 1) (n + 5) is a multiple of 3 for all n ϵ N.