16. Find the value of
$$
\frac{1}{1+11^{-2011}}+\frac{1}{1+11^{-2009}}+\frac{1}{1+11^{-2007}}+\cdots+\frac{1}{1+11^{2009}}+\frac{1}{1+11^{2011}} .
$$
16. Answer: 1006
The series can be paired as
$$
\left(\frac{1}{1+11^{-2011}}+\frac{1}{1+11^{2011}}\right)+\left(\frac{1}{1+11^{-2009}}+\frac{1}{1+11^{2009}}\right)+\cdots+\left(\frac{1}{1+11^{-1}}+\frac{1}{1+11^{1}}\right) .
$$

Each pair of terms is of the form
$$
\frac{1}{1+a^{-1}}+\frac{1}{1+a}=1 .
$$

There are 1006 pairs of such terms, and thus the sum of the series is 1006 .