Question

prove that the sum of three consecutive even numbers is divisible by 6.​

Answer 1

Step-by-step explanation:

If you see the any three consecutive numbers, you can figure out atleast one of them is divisible by 6. We can use mathematical induction for proving it mathematically. For a number to be divisible by 6, it should be divisible by 2 and 3. Since all are even numbers, the number will be divisible by 2.

Answer 2

Let three consecutive even numbers be 2n-2 , 2n and 2n+2

their sum is S=(2n-2)+(2n)+(2n+2)=6n

which is divisible by 6

Hence the sum of any 3 consecutive even numbers is divisible by 6.