+41 Define $a \ \# \ b$ as the arithmetic mean of $a$ and $b$. What is the value of $((1\ \#\ 2)\ \#\ 3) \ \# \ 4$? Express your answer as a common fraction.
+80 I'm sure this is a trick question, but I guess I can try.
Order of operations first:
mean of 1 and 2 is
\((1+2)/2=1.5\)
mean of 1.5 and 3 is
\((1.5+3)/2 =4.5/2 =2.25\)
mean of 2.25 and 4 is
\((2.25+4)/2 =6.25/2 =3.125\)
so the final answer is \(\fbox{3.125}\)
