[tex]\begin{equation}\text { Question: Find the value of } \frac{1}{1+x}+\frac{2}{1+x^{2}}+\frac{2^{2}}{1+x^{4}}+\ldots \cdot \frac{2^{100}}{1+x^{200}}\end{equation}[/tex]

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Аноним Аноним · Answer 1 · 2022-04-08T21:01:08+02:00

[tex]\bold{Heya!}[/tex]

Your answer to this is:

[tex]\sf{= \frac{1}{2} \: + \frac{2}{1 \: + \: x^2} \: + \: \frac{1}{1 \: + \: x^4} \: + \: \frac{2^1^0^0}{1 \: + \: x^2^0^0}[/tex]

[tex]\sf{= \frac{1}{2} \: + \frac{2}{1 \: + \: x^2} \: + \: \frac{1}{1 \: + \: x^4} \: + \: \frac{2^1^0^0}{1 \: + \: x^2^0^0} \: (1)[/tex]

[tex]\sf{Apply \: rule:} \: (a) = a[/tex]

[tex]\sf{(1) = 1[/tex]

[tex]\sf{= \frac{1}{2} \: + \frac{2}{1 \: + \: x^2} \: + \: \frac{1}{1 \: + \: x^4} \: + \: \frac{2^1^0^0}{1 \: + \: x^2^0^0} \: ^. \: 1[/tex]

[tex]\sf{\frac{1}{1 \: + \:1} = \frac{1}{2}[/tex]

[tex]\sf{\frac{2^1^0^0}{1 \: + \: x^2^0^0} ^.^ \: 1 \: = \: \frac{2^1^0^0}{1 \: + \: x^2^0^0}[/tex]

[tex]\sf{= \frac{1}{2} \: + \frac{2}{1 \: + \: x^2} \: + \: \frac{1}{1 \: + \: x^4} \: + \: \frac{2^1^0^0}{1 \: + \: x^2^0^0}[/tex]

Hopefully This Helps ! ~

#LearnWithBrainly

[tex]\underline{Answer :}[/tex]

Jaceysan ~