N is a positive integer

i) Explain why n (n+1) must be an even number?

ii) Explain why 2n-1 must be an odd number?

Step-by-step explanation:

product of two consecutive numbers is always even.

n (n+1)

case 1

if n is odd, let n=2k+1, where k is an integer

n+1=2k+1+1=2k+2=2 (k+1)

n (n+1) = (2k+1) [2 (k+1) ]=2 (2k+1) (k+1) = even number.

case 2

if n is even, let n=2m, where m is an integer.

n+1=2m+1

n (n+1) = 2m (2m+1) = even integer.

so in both cases n (n+1) is even.