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For how many integers where 2 <= n <= 100 is n(n + 1) odd?

 Oct 22, 2021
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For how many integers where 2 <= n <= 100 is n(n + 1) odd?     

 

Let's see if we can detect a trend  

 

    n        n + 1        Product  

 

    2           3                6  

    3           4              12  

    4           5              20  

    5           6              30  

    6           7              42    

 

I don't think we have to go any further to see what's always going to happen.  

This illustrates that no matter what n equals, then either n or n+1 will always be even.  

The product of an even number and any other number is always even.   

 

The answer to the problem is NONE of them will be odd.   

.

 Oct 22, 2021
edited by Guest  Oct 22, 2021

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