dynamical list problem

[Thomas Klemm]

(01-02-2019 04:36 PM)peacecalc Wrote:  I have a problem for you, but no solution.

You could create the following list from {1 2 1 3 2}:

\(\left \{ 1 \frac{1}{2} \frac{1}{2} 1 \frac{1}{3} \frac{1}{3} \frac{1}{3} \frac{1}{2} \frac{1}{2} \right \}\)

And then just use a moving window of 5 elements and add them up:

\(\begin{matrix}
\left \{ 1+\frac{1}{2}+\frac{1}{2}+1+\frac{1}{3} \right \} & = 3 \frac{1}{3} \\
\left \{ \frac{1}{2}+\frac{1}{2}+1+\frac{1}{3}+\frac{1}{3} \right \} & = 2 \frac{2}{3} \\
\left \{ \frac{1}{2}+1+\frac{1}{3}+\frac{1}{3}+\frac{1}{3} \right \} & = 2 \frac{1}{2} \\
\left \{ 1+\frac{1}{3}+\frac{1}{3}+\frac{1}{3}+\frac{1}{2} \right \} & = 2 \frac{1}{2} \\
\left \{ \frac{1}{3}+\frac{1}{3}+\frac{1}{3}+\frac{1}{2}+\frac{1}{2} \right \} & = 2 \\
\end{matrix}\)

You end up with:

\(\begin{matrix}
5 \div \frac{10}{3} & = \frac{3}{2} & = 1.500\\
5 \div \frac{8}{3} & = \frac{15}{8} & = 1.875 \\
5 \div \frac{5}{2} & = 2 & = 2.000 \\
5 \div \frac{5}{2} & = 2 & = 2.000 \\
5 \div 2 & = \frac{5}{2} & = 2.500
\end{matrix}\)

Now you have additional intermediate values but they might still be useful for you.

Cheers
Thomas