Let $P (n)$ be the statement $" 3^{n} > n "$ . If $P (n)$ is true, $P (n + 1)$ is true.

True

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False

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Solution

The correct option is A True
$P (n)$ is true.
$3^{n} > n$
${3.3}^{n} > 3 n$
$3^{n + 1} > n + 2 n$
$3^{n + 1} > n + 1$ $[2 n > 1$ for every $n \in N ⟹ 2 n + n > n + 1$ for every $n \in N]$
$P (n + 1)$ is true.

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