The sum of series \( \frac{1}{x+1}+\frac{2}{x^{2}+1}+\frac{2^{2}}{x^{4}+1}+\ldots+\frac{2^{100}}{x^{2^{100}}+1} \) when \( x=2 \) is:
\( 1-\frac{2^{100}}{4^{100}-1} \)
\( 1-\frac{2^{101}}{4^{101}-1} \)
\( 1+\frac{2^{101}}{4^{101}-1} \)
\( 1+\frac{2^{100}}{4^{101}-1} \)
