Prove that 2
divides n²+n where n is a
positive integer
Answers
Answered by
14
Step-by-step explanation:
n
2
−n=(2q)
2
−2q=4q
2
−2q=2q(2q−1)
n
2
−n=2r , where r=q(2q−1)
n
2
−n is divisible by 2 .
Case ii: Let n be an odd positive integer.
When n=2q+1
In this case
n
2
−n=(2q+1)
2
−(2q+1)=(2q+1)(2q+1−1)=2q(2q+1)
n
2
−n=2r, where r=q(2q+1)
n
2
−nis divisible by 2.
∴ n
2
−n is divisible by 2 for every integer n
Hope it is helpful to you
Answered by
5
Answer:
ANSWER
Case i: Let n be an even positive integer.
When n=2q
In this case , we have
n
2
−n=(2q)
2
−2q=4q
2
−2q=2q(2q−1)
n
2
−n=2r , where r=q(2q−1)
n
2
−n is divisible by 2 .
Case ii: Let n be an odd positive integer.
When n=2q+1
In this case
n
2
−n=(2q+1)
2
−(2q+1)=(2q+1)(2q+1−1)=2q(2q+1)
n
2
−n=2r, where r=q(2q+1)
n
2
−nis divisible by 2.
Similar questions