Question

the product of two consecutive positive integer is divided by 2​

Answer 1

Answer:

3

Step-by-step explanation:

two consecutive integer=2,3

product=2x3=6

division=6÷2=3

Answer 2

${\mathfrak{\pink{\underline{\underline{Solution:-}}}}}$

$\sf{Let\;n\;and\;n-1\;be\;the\;two\;positive\;integers.}$

$\sf{Product = n(n-1)=n^{2}-n}$

$\bf{CASE-1\;(when\;n\;is\;even)}$

$\sf{Let\;n=2q}$

$\sf{n^{2}-n=(2q)^{2}-2q}$

$\sf{=4q^{2}-2q}$

$\sf{=2q(2q-1)}$

$\sf{Hence\;the\;product\;n^{2}-n\;is\;divisible\;by\;2}$

$\bf{CASE-2\;(when\;n\;is\;odd)}$

$\sf{Let\;n\;be\;2q+1}$

$\sf{n^{2}-n=(2q+1)^{2}-(2q+1)}$

$\sf{=4q^{2}+4q+1-2q-1}$

$\sf{=4q^{2}+2q}$

$\sf{=2q(2q+1)}$

$\sf{Hence\;the\;product\;n^{2}-n\;is\;divisible\;by\;2}$

Hence, we can conclude that the product of two consecutive positive integers is always divisible by 2.