this is for holding javascript data
Dat Do edited beginproblem_a_You_a.tex
about 10 years ago
Commit id: 4a03614d7e9a56387e3564f3102b5a2d4114c2a1
deletions | additions
diff --git a/beginproblem_a_You_a.tex b/beginproblem_a_You_a.tex
index f9b8337..6d25323 100644
--- a/beginproblem_a_You_a.tex
+++ b/beginproblem_a_You_a.tex
...
\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 $\sum\limits_{i=1}^n i*2^{n-i} = 2^{n+1}-n-2$