Convergence in Normed Dual Space implies Weak-* Convergence/Proof 1

Proof
From Convergent Sequence in Normed Vector Space is Weakly Convergent, $\sequence {f_n}_{n \mathop \in \N}$ converges weakly.

From Weakly Convergent Sequence in Normed Dual Space is Weakly-* Convergent, $\sequence {f_n}_{n \mathop \in \N}$ converges weakly-$\ast$.