Checking the differences:
11 - 5 = 6
12 - 11 = 1
16 - 12 = 4
21 - 16 = 5
26 - 21 = 5
32 - 26 = 6
Difference series: 6, 1, 4, 5, 5, 6, __, 7, 16
The missing number follows the pattern and should be 41.
41
The value of $ \frac{1}{1 + p^{(y-z)} + p^{(x-z)}} + \frac{1}{1 + p^{(x-y)} + p^{(z-y)}} + \frac{1}{1 + p^{(y-x)} + p^{(z-x)}}, $ is:
Simplify the following expression: $ \frac{2^{n+5} - 4 \cdot 2^{n}}{2 \cdot (2^{n+4})} $.