Question

for any positive integer n, prove that ${n}^{3} - n \:$ is divisible by 6....

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Answer 1

Answer..

Step by step explanation..

To prove

n^3 -n is divisible by 6

where n is any + ve integer.

So , let n = 2

2^3 -2 = 6

6 is divisible by 6.

let n as 3

3^3-3 = 24

24 is also divisible by 6.

let n as 4

4^3 -4 = 60

60 is also divisible by 6.

So from the above cases we can prove that n ^ 3 -n is divisible by 6 .

Where n is any+ve integer.