24pateldheer 24pateldheer

02-06-2019
Mathematics

contestada

Prove that for all whole values of n the value of the expression:
n(n–1)–(n+3)(n+2) is divisible by 6.

Prove that for all whole values of n the value of the expression nn1n3n2 is divisible by 6 class=

Respuesta :

LammettHash LammettHash

03-06-2019

Expand:

[tex]n(n-1)-(n+3)(n+2)=(n^2-n)-(n^2+5n+6)=-6n-6[/tex]

Then we can write

[tex]n(n-1)-(n+3)(n+2)=6\boxed{(-n-1)}[/tex]

which means [tex]6\mid n(n-1)-(n+3)(n+2)[/tex] as required.

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