Question

For any positive integer n prove that n³-n is divisible by 6​

Answer 1

Answer:

→ (n³-n)

Put n = 1,

(1³-1) = 1-1 = 0 is divisible by 6

Put n = 2,

(2³-2) = 8-2 = 6 is divisible by 6

Put n = 3,

(3³-3) = 27-3 = 24 is divisible by 6

Put n = 4,

(4³-4) = 64-4 = 60 is divisible by 6

Therefore,For any positive integer 'n', (n³ -n) is divisible by 6.