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If Sn is the nth partial sum of the harmonic series, show that e^Sn > n+1. Why does this imply that the harmonic series is divergent?
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If Sn is the nth partial sum of the harmonic series, show that e^Sn > n+1. Why does this imply that the harmonic series is divergent?
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Apr 7, 2018
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if Sn is the nth partial sum of the harmonic series, show that e^Sn > n+1. Why does this imply that the harmonic series is divergent?
Mathematics
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Morten Jensen
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You have
so showing that
amounts to the same as showing that
.
As
, you have
. By comparison, then, it follows that
at a faster rate, which means
must diverge.
Filype
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Apr 13, 2018
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Filype
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