Dat Do edited beginproblem_a_You_a.tex  about 10 years ago

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\item $W(4) = 26$  \item $W(5) = 57$  \end{itemize}  We know that the closed form expression should involve a value slightly larger than $2^n$, so we try: try the same $n$ values for:  $2^{n+1}$ and get \begin{itemize} \item $n $2^{1+1}  = 1$ as $4$ 4$  \item $n $2^{2+1}  = 2$ as $8$ 8$  \item $n $2^{3+1}  = 3$ as $16$ 16$  \item $n $2^{4+1}  = 4$ as $32$ 32$  \item $n $2^{5+1}  = 5$ as $64$ 64$  \end{itemize}  The difference between $2^{n+1}$ and $W(n)$ appears to be $-n-2$ for each term, so the closed form expression for $W(n)$ must be $\sum\limits_{i=1}^n i*2^{n-i} = 2^{n+1}-n-2$