After three hours of hard work Henry has succeeded in provin

After three hours of hard work, Henry has succeeded in proving the following theorem: If sigma_n=0^infinity a_n convergent then lim a_n = 0. After three more hours of hard work, he has managed to prove: If lim a_n notequalto 0, then sigma_n = 0^infinity is not convergent. What would you say to Henry?

Solution

the second statement is just contrapositive statement of first statement. And Statement(or implication) is always equals to its contrapostive statement.

that is,

p --> q = ~ q --> ~p