Problem 358 (difficulty: 4/10)

Find a sequence \(\displaystyle a_n\) such that \(\displaystyle \sum a_n\) is convergent, and \(\displaystyle a_{n+1}/a_n\) is not bounded.

Solution:

For example \(\displaystyle a_{2n}=\frac1{n^2}\) and \(\displaystyle a_{2n+1}=\frac1{n^3}\).

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