Analysis: First of all, because n is a positive even number, it is meaningless to substitute n=k+ 1 if the proposition is assumed to be true when proving by mathematical induction, so it is necessary to prove that n=k+2 is true.

Solution: If the proposition is true when n=k(k≥2, k is even), it is necessary to prove that n=k+2 is true, because n can only take even numbers.

So choose B.