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Let $P (n) : n^{2} + n + 1$ is an even integer. If P(k) is assumed true then P(k+ 1) is true. Therefore P(n) is true.

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none of these

for all $n \in N$

for n > 1

for n > 2

answer is D.

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Detailed Solution

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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