Prove that for any positive integer number $\mathrm{n}, \mathbf{n}^3+\mathbf{2} \mathbf{n}$ is divisible by 3 .

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written 3.1 years ago by

prajapatijaimin • 3.3k

modified 3.1 years ago by

sagarkolekar ★ 11k

discrete structures and graph theory

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1 Answer

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written 3.1 years ago by

prajapatijaimin • 3.3k

Solution:

Let $S(n)=n^3+2 n$ is divisible by 3 .

Step 1:

Inductive base: for $n=1$

$(1)^3+2.1=3$ which is divisible by 3

Thus, $s(1)$ is true.

step2 :

Inductive hypothesis: Let $s(k)$ is true ide. $k^3+2 k$ is divisible by 3 holds true.

$ \text { or, } k^3+2 k=3 s …

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