Question

Show that one and only one out of n, n+1 or n+2 is divisible by3, where n is any positive integer

Answer 1

Answer:

Step-by-step explanation:

Put the value of n=1

So,1,1+1,1+2

1,2,3 out of these one is divisible by 3

n=2

So,2,2+1,2+2

2,3,4 out of this also one is divisible by 3

Similarly put the values of n

We observe that out of each triplet one and only one no. Which is multiple of 3 i.e., divisible by 3

Hence,one and only one out of n,n+1 and n+2 is divisible by 3, where n is any positive integer

HOPE U WILL GET IT

Answer 2

:

Let a be any positive integer and b=3,so by Euclid division lemma a=bq+r

a=3q+r ,therefore the possible remainder are 0,1,2

Let n=0

So a=3q+0;which is divisible by 3

Let n=1

So,a=3q+1,not divisible by 3 and when n=1

a=3q+2,which is not divisible by 3

Hence prove

Hope u got it