$\begin{array}{l}\text { 1. Let } g(x)=\ln \left(2^{x}+1\right) \text {. Then } \\ g(-4)-g(-3)+g(-2)-g(-1)+ \\ g(1)-g(2)+g(3)-g(4) \\ =\end{array}$
- 1. $-2 \ln 2$.

From the problem, we know
$$
g(x)-g(-x)=\ln \frac{1+2^{x}}{1+2^{-x}}=x \ln 2 \text {. }
$$

Therefore, the required value is $-2 \ln 2$.