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If x<1,p rov et h a t 1/(1+x)+(2x)/(1+x...

If `x<1,p rov et h a t` `1/(1+x)+(2x)/(1+x^2)+(4x^3)/(1+x^4)+oo=1/(1-x)`

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To prove that \[ \frac{1}{1+x} + \frac{2x}{1+x^2} + \frac{4x^3}{1+x^4} + \ldots = \frac{1}{1-x} \] for \( x < 1 \), we can follow these steps: ...
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