Question:
If P (n) is the statement "n3 + n is divisible by 3", prove that P (3) is true but P (4) is not true.
Solution:
We have:
$P(n): n^{3}+n$ is divisible by 3 .
Thus, we have :
$P(3)=3^{3}+3=27+3=30$
It is divisible by $3 .$
Hence, $P(3)$ is true.
Now,
$P(4)=4^{3}+4=64+4=68$
It is not divisible by 3 .
Hence, $P(4)$ is not true.
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