Suppose we want to prove that: 1/2 * 3/4 ... 2n-1/2n < 1/sqrt(3n)

for all positive integers.

(a) Show that if we try to prove this inequality using mathematical induction, the basis step works, but

the inductive step fails.

(b) Show that mathematical induction can be used to prove the stronger inequality: 1/2 * 3/4 ... 2n-1/2n < 1/sqrt(3n+1)

So far I have proven the basis step works in part a by plugging in 1, however, I do not know how to say the inductive step fails. I have no clue on part b. Thanks.