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  • Prove that is divisible by 2 for any positive integer n.      

Prove that n^2+n is divisible by 2 for any positive integer n.

 

 

 

 
 
 
 
 

Answers (1)

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

n^2+n=(2q)^2+2q

                =4q^2+2q

                =2q(2q+1)

which is divisible by 2.

when n=2q+1

n^2+n = (2q+1)^2+(2q+1)

                = 4q^2+4q+1+2q+1

                = 4q^2+6q+2

                = 2(2q^2+3q+1)

Hence n^2+n is divisible by 2 for any positive integer.

 

Posted by

Ravindra Pindel

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