Question

prove that the product of two positive consecutive integers is divisible by 2.​

Answer 1

Answer:

Let the two consecutive positive integers be x and x+1

Let x=2a (even)     and x+1 =2a+1(odd)

According to the given question

Product of two integers (x)(x+1)

=x^2+x

Case 1: if x is an even number

By putting the values

We have

x^2+x=2a^2+2a

=2a (a+1)

Check and divide the above expression by 2

= 2a (a+1)/2

We get a (a+1)

Hence it is clearly proved that the product of 2 integers are divisible by 2

Case 2: If x is an odd number

By putting the values x=2a+1

We have

x^2+x=(2a+1)^2+2a+1

=4a^2+1+4a+2a+1

=4a^2+6a+2

=2(2a^2+3a+1)

Re Check: Divide the above expression by 2

=2(2a^2+3a+1)/2

We get

2a^2+3a+1

Hence proved

Hope it helps!

Answer 2

Answer:

lets take 2 consecutive integers 1,2, THEN1*2=2

IF WE TAKE 2 AND3 , THEN 2*3=6

Step-by-step explanation:

LIKEWISE WE CAN PROVE