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

MCQ

Let $P(m)$ be the statement $\mathrm{m}^2>100$, 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(k) is true

Solution:
$\Rightarrow r^2>100 \Rightarrow r^2+2 r+1>100+2 r+1 \\
& \Rightarrow(r+1)^2>100 \\
& \Rightarrow P(r+1) \text { is true as } \\
& \left.r^2+(2 r+1)>r^2>100 \Rightarrow P(k+1) \text { is true (say } r=k\right)$
$P(k+1)$ is true when every $p(k)$ is
So, In order to prove that $P(k+1)$ is true.
It is sufficient to consider $\mathrm{P}(\mathrm{k})$ is true.

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