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Question: Answered & Verified by Expert
If ' $n$ ' is a positive integer, then $\mathrm{n}^{3}+2 \mathrm{n}$ is divisible by
MathematicsMathematical InductionKCETKCET 2009
Options:
  • A 2
  • B 6
  • C 15
  • D 3
Solution:
1273 Upvotes Verified Answer
The correct answer is: 3
Let $P(n)=n^{3}+2 n$
$$
\begin{array}{lc}
\Rightarrow & \mathrm{P}(1)=1+2=3 \\
\Rightarrow & \mathrm{P}(2)=8+4=12 \\
\Rightarrow & \mathrm{P}(3)=27+6=33
\end{array}
$$
Here, we see that all these numbers are divisible by 3 .

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