- #1

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## Homework Statement

I have been asked to prove the convergence or otherwise of ∑

^{∞}

_{n=1}n/(3n + n

^{2}).

In the example solution, with the aim to prove divergence by comparison with the Harmonic Series, the lecturer has stated that n/(3n + n

^{2}) ≥ n/(4n

^{2}) = 1/4n and which diverges to +∞.

I was wondering how to arrive at the decision to write n/(3n + n

^{2}) ≥ n/(4n

^{2}) came from, and how I would arrive at a similar inequality in further examples.