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\sum_1^\infty\frac{x^n}{1+x^n} [/tex] converges when x is in [0,1)

[tex]

\sum_1^\infty\frac{x^n}{1+x^n} = \sum_1^\infty\frac{1}{1+x^n} * x^n <= \sum_1^\infty\frac{1}{1} * x^n = \sum_1^\infty x^n [/tex]

The last sum is g-series, converges since r = x < 1

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# Convergent series. Is my logic correct?

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