1. (5 marks) A subgroup N of a group G is said to be normal if and only if every left coset of N is equal to the corresponding right coset, i.e., k G k N = N k Find all subgroups of the dihedral group D 3 . For each subgroup, determine whether it is normal or not. Prove all your claims. 2. (5 marks) Let a be a non-negative real number. Prove that the series n = 1 ( n + 1 an + 2 ) n 2 converges when a < 1 and diverges when a 1 ..