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

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

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