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True or False
If ∑n=1∞an\displaystyle \sum_{n=1}^{\infty} a_nn=1∑∞an is a convergent series of positive real numbers, then so is ∑n=1∞annn+1\displaystyle \sum_{n=1}^{\infty} a_n^{\frac{n}{n+1}}n=1∑∞ann+1n.
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