Question

show that product of 3 consecutive positive integer is 6​

Answer 1

Answer:

Please find the attached image.

Step-by-step explanation:

Answer 2

Answer:

product of 3 consecutive positive integer is divisible 6

Step-by-step explanation:

Let say Three consecutive integers are

3n , 3n + 1 , 3n + 2

Products = 3n(3n + 1)(3n + 2)

= 3n ( 9n² + 9n + 2)

= 3n ( 9n(n+1)  + 2)

n can be 2k or 2k+1

if n = 2k

= 3 * 2k (9*2k(2k +1) + 2)

= 6 k ( 18k(k+1) + 2)

Divisible by 6

if n = 2k + 1

= 3 (2k + 1) ( 9 (2k + 1)(2k + 2)  + 2)

= 3 (2k + 1) 2 ( 9 (2k + 1)(k+1) + 1)

= 6 (2k + 1) ( 9 (2k + 1)(k+1) + 1)

Divisible by 6

Hence product of three consecutive positive integer is divisible by