How do I show that if $\displaystyle \sum \frac{x_n}{x_1 + x_2 + \dots + x_n}$ converges then $\displaystyle \sum x_n$ converges.
I was able to prove it the other way around, but I'm stuck for this one.
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4Are $x_{n}$'s all positive? – Seewoo Lee Apr 25 '18 at 15:45
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2If $x_n>0$ then see https://math.stackexchange.com/questions/808964/divergence-of-sum-limits-k-1n-fraca-ns-n-where-s-n-sum-limits-k – Robert Z Apr 25 '18 at 15:56
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Yes, I believe all $x_n$'s are positive. – sedrick Apr 25 '18 at 16:14