Question

prove that n×n-n is divisible by 2 or any positive integer

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Answer 1

Here is the answer to your question.

 Any positive integer is of the form 2q or 2q + 1, where q is some integer

When n = 2q, 

n²+n=(2q)²+2q

      =4q²+2q

      = 2q(2q+1)   

which is divisible by 2

 

when n=2q+1

n²-n=(2q+1)²+(2q+1)

      = 4q²+4q+1+2q+1

      =4q²+6q +2

     =  2(2q²+3q+1)

which is divisible by 2

hence n²+n is divisible by 2 for every positive integer n

Answer 2

Answer:

please correct your question    NOT  or    THAT IS   for

Step-by-step explanation:

for any positive integer  n

n-1 and n are consecutive integers

n or n -1 is even number

n[n-1] is even number

nxn - n is even number

n×n-n is divisible by 2