Question

1%7D%7B1%2Bx%7D%2B%5Cfrac%7B2%7D%7B1%2Bx%5E%7B2%7D%7D%2B%5Cfrac%7B2%5E%7B2%7D%7D%7B1%2Bx%5E%7B4%7D%7D%2B%5Cldots%20%5Ccdot%20%5Cfrac%7B2%5E%7B100%7D%7D%7B1%2Bx%5E%7B200%7D%7D%5Cend%7Bequation%7D" id="TexFormula1" title="\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}" alt="\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}" align="absmiddle" class="latex-formula">

Answer 1

$\bold{Heya!}$

Your answer to this is:

$\sf{= \frac{1}{2} \: + \frac{2}{1 \: + \: x^2} \: + \: \frac{1}{1 \: + \: x^4} \: + \: \frac{2^1^0^0}{1 \: + \: x^2^0^0}$

→ EXPLANATION :-

$\sf{= \frac{1}{2} \: + \frac{2}{1 \: + \: x^2} \: + \: \frac{1}{1 \: + \: x^4} \: + \: \frac{2^1^0^0}{1 \: + \: x^2^0^0} \: (1)$

$\sf{Apply \: rule:} \: (a) = a$

$\sf{(1) = 1$

$\sf{= \frac{1}{2} \: + \frac{2}{1 \: + \: x^2} \: + \: \frac{1}{1 \: + \: x^4} \: + \: \frac{2^1^0^0}{1 \: + \: x^2^0^0} \: ^. \: 1$

$\sf{\frac{1}{1 \: + \:1} = \frac{1}{2}$

$\sf{\frac{2^1^0^0}{1 \: + \: x^2^0^0} ^.^ \: 1 \: = \: \frac{2^1^0^0}{1 \: + \: x^2^0^0}$

$\sf{= \frac{1}{2} \: + \frac{2}{1 \: + \: x^2} \: + \: \frac{1}{1 \: + \: x^4} \: + \: \frac{2^1^0^0}{1 \: + \: x^2^0^0}$

Hopefully This Helps ! ~

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$\underline{Answer :}$

Jaceysan ~