First slide

Introduction to P.M.I

Question

Let $P (n) : n^{2} + n + 1$ is an even integer. If p(k) is assumed true $\Rightarrow P (k + 1)$ is true. Therefore, P(n) is TRUE

Easy

A

for n>1
B

for all $n \in N$
C

for n>2
D

None of the above

Solution

Given, $P (n) : n^{2} + n + 1$
At n = 1, P(1):3, which is not an even integer.
P(1 ) is not true (principle of induction is not applicable).
Also, n(n + 1 ) + 1 is always an odd integer.

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