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If x1,x2,x3,…x_1,x_2,x_3,\ldotsx1,x2,x3,… is a sequence of positive reals such that ∑k=1∞xk\displaystyle \sum_{k=1}^\infty x_kk=1∑∞xk converges, does ∑k=1∞(exk−1)\sum_{k=1}^{\infty}\left(e^{x_k}-1\right)k=1∑∞(exk−1) converge?
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