Question

Prove: The square of the sum of

two consecutive integers is odd.
(n + (n + 1))2= ([ ? ]n + 1)2
= [ ]n2 + [ ]n + []
= 2([ ]n2 + [ ]n) + 1
= odd

Answer 1

(n + (n + 1))²

= (2n + 1)²

= 4n² + 4n + 1

= 2(2n² + 2n) + 1

= odd