2017-07 Supremum of a series

For \( \theta>0 \), let
\[
f(\theta) = \sum_{n=1}^{\infty} \left( \frac{1}{n+ \theta} – \frac{1}{n+ 3\theta} \right).
\]
Find \( \sup_{\theta > 0} f(\theta) \).

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2017-07 Supremum of a series, 1.6 out of 5 based on 51 ratings