8. A sequence of distributions $\left(F_{n} ight)$ converges to a distribution $F$ if $\left\langle F_{n}, phi ight angle ightarrow\langle F, \phi angles for all test functions $\phi$. (1) Show that if $F_{n} ightarrow F$ then $F_{n}^{\prime] ightarrow F^{\prime}$. (ii) This limiting process applies to the partial sums ($n$ terms) of a series. Define $F(x)=x$ for $-\pi