Question

for any positive integer n prove that n cube -n is divisible by 6​

Answer 1

solution is in aatachment

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Answer 2

Answer:

let -

a=n3-n

= n(n2-1)

=n(n-1)(n+1)

=(n-1)n(n+1)

Step-by-step explanation:

1)Now out of there (n-1),n and (n+1) one must be even so a is divisible by 2

2)Also (n-1),n and (n+1) are three consecutive integers thus as proved a must be divisible by 3

from (1)and (2)

a must be divisible by 2×3=6

Hence n3-n is divisible by 6 for any positive integer n...

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