Sum Of Minuscule Differences

Calculus

Let {Un}n=1n=∞\left \{U_n\right \}_{n=1}^{n=\infty} be a sequence of positive numbers such that ∑n=1∞Un \displaystyle \sum_{n=1}^\infty U_n converges.
Is it also true that ∑n=1∞(eUn−1) \displaystyle \sum_{n=1}^\infty \left( e^{U_n} - 1 \right) also converges?

Jose Sacramento by Jose Sacramento
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