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infinite abs sum is divergent for sequence in R+

Source: VTRMC 2004 P7

July 27, 2021
limitsreal analysis

Problem Statement

Let {an}\{a_n\} be a sequence of positive real numbers such that lim⁡n→∞an=0\lim_{n\to\infty}a_n=0. Prove that ∑n=1∞∣1−an+1an∣\sum^\infty_{n=1}\left|1-\frac{a_{n+1}}{a_n}\right| is divergent.
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