Answer
The property was proved for $n=1$
The property is correct if n is changed by $n+1$
Work Step by Step
Let's prove the property for $n=1$:
$n^2+n=1^2+1=2$
2 is divisible by 2. It is correct!
Suppose that the propety is correct, that is:
$n^2+n$ is divisible by 2 for all natural numbers.
Now, let's prove the property for $n+1$:
$(n+1)^2+(n+1)=n^2+2n+1+n+1=(n^2+n)+(2n+2)=(n^2+n)+2(n+1)$
Both terms are divisible by 2. So, the sum is also divisible by 2.
