If (n+1)^2 is even then n is odd. Find what proof works best with this question

Sincere Garcia

Sincere Garcia

Answered question

2022-10-03

If ( n + 1 ) 2 is even then n is odd
find what proof works best with this question

Answer & Explanation

Jordan Owen

Jordan Owen

Beginner2022-10-04Added 7 answers

If ( n + 1 ) 2 is even, then n + 1 is even, and so n is odd.
s2vunov

s2vunov

Beginner2022-10-05Added 2 answers

Assume n is even. So n = 2 k, for some integer k. Then ( n + 1 ) 2 = n 2 + 2 n + 1 = ( 2 k ) 2 + 2 ( 2 k ) + 1 = 4 k 2 + 4 k + 1 = 2 ( 2 k 2 + 2 k ) + 1 = 2 m + 1, which is an odd integer, (noting that we can represent m = 2 k 2 + 2 k, another integer, given that k is an integer.)

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