Prove that 2n^3 + 3n^2 + n is divisible by 6 for every integer n > 1 by mathematical induction. (7 marks)

The answer is True

Step-by-step explanation:

A mathematical induction consists in only 2 steps:  

First step: Show the proposition is true for the first one valid integer number.

Second step: Show that if any one is true then the next one is true  

Finally, if first step and second step are true, then the complete proposition is true.

So, given

First step: using and replacing n=2 (the first valid integer number >1)

As the result is an integer number, so the first step is true.

Second step: using any next number, , let it replace

As the First step is true, we know that

,

So let it replace in the previous expression

Finally

where the last expression is an integer number

So the second step is true, and the complete proposition is True

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