Question

prove that 1 of any 3 cosicutive positive integer must be divided by 3 class 10 thmaths real number chapter

Answer 1

Let three consecutive positive integers be n, =n + 1 and n + 2Whenever 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. 

Answer 2

let the no. be n ,so
n= 3q^
so n is divisible by 3 because 3q^ is also divisible by 3
now,
n= 3q^ +1

here ,n is not divisible by 3 because when 3q^+1 is divided by 3 it leaves 1 as remainder

now,
n=3q^+2
here , n is not divisible by 3 because when 3 is divided by 3q^+2 then it leaves 2 as remainder
hence proved that 1 of any positive cosecutive integer is divisible by 3.