Problem $(1$pt$)$ Prove that the total number of parenthesizations of $n$ matrices is $(\frac{4^n}{n^{\frac{3}{2}}}).$ Your

proof should be self$-$contained and elementary. Only the results given in Chapter $3$ and C$.4$ in the

textbook $(3$rd edition$)$ can be used. That is$,$ if you use a non$-$obvious claim that is not in Chapter $3$

or C$\mathrm{.}4,$ you have to prove it$.$

textbook reference: introduction to algorithms, third edition by thomas h$.$ cormen, charles e$.$leiserson, ronald l$.$rivest, clifford stein