Let P(m) be the statement m^2 > 100, the statement P(k + 1) will … - Vidyadip

MCQ

Let $P(m)$ be the statement $m^2 > 100$, the statement $P(k + 1)$ will be true if:

A
$P(1)$ is true
B
$P(2)$ is true
✓
$P(k)$ is true
D
none of these

✓

Answer

Correct option: C.

$P(k)$ is true

$P(r)$ is true
$ \Rightarrow r^2>100$
$\Rightarrow r^2+2 r+1>100+2 r+1 $
$ \Rightarrow(r+1)^2>100 $
$ \Rightarrow P(r+1) $ is true as
$r^2+(2 r+1)>r^2>100$
$\Rightarrow P(k+1)$ is true $($say $r=k)$
$P(k + 1)$ is true when every $p(k)$ is
So, In order to prove that $P(k + 1)$ is true.
It is sufficient to consider $P(k)$ is true.

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