Problem 77E

77. In Example 9 we showed that the harmonic series is divergent. Here we outline another method, making use of the fact that $e^{x}>1+x$ for any $x>0$. (See Exercise 6.2.109.) If $s_{n}$ is the $n$ th partial sum of the harmonic series, show that $e^{s_{n}}>n+1$. Why does this imply that the harmonic series is divergent?

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