- #1
emilkh
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\sum_1^\infty\frac{x^n}{1+x^n} converges when x is in [0,1)
<br /> \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
The last sum is g-series, converges since r = x < 1
<br /> \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
The last sum is g-series, converges since r = x < 1
