10.Prove that one of every three consecutive positive integers is divi

1.	10.Prove that one of every three consecutive positive integers is divisible by 3.
Answer» Ans :- Let three consecutive positive integers be n, n + 1 and n + 2 Whenever a number is divided by 3, the remainder obtained is either 0 or 1 or 2 ∴ n = 3p or 3p + 1 or 3p + 2, where p is some integer. If n = 3p, then n is divisible by 3. If n = 3p + 1, then n + 2 = 3p + 1 + 2 = 3p + 3 = 3(p + 1) is divisible by 3. If n = 3p + 2, then n + 1 = 3p + 2 + 1 = 3p + 3 = 3(p + 1) is divisible by 3 So, we can say that one of the numbers among n, n + 1 and n + 2 is always divisible by 3. thanks

10.Prove that one of every three consecutive positive integers is divisible by 3.

Answer»

Ans :- Let three consecutive positive integers be n, n + 1 and n + 2

Whenever a number is divided by 3, the remainder obtained is either 0 or 1 or 2

∴ n = 3p or 3p + 1 or 3p + 2, where p is some integer.

If n = 3p, then n is divisible by 3.

If n = 3p + 1, then n + 2 = 3p + 1 + 2 = 3p + 3 = 3(p + 1) is divisible by 3.

If n = 3p + 2, then n + 1 = 3p + 2 + 1 = 3p + 3 = 3(p + 1) is divisible by 3

So, we can say that one of the numbers among n, n + 1 and n + 2 is always divisible by 3.

thanks