Let be a convergent series of positive terms. Prove that there exists a **strictly increasing** sequence which is also **unbounded** such that the series also converges.

**Solution**

We set and we observe that

That’s all folks.

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Let be a convergent series of positive terms. Prove that there exists a **strictly increasing** sequence which is also **unbounded** such that the series also converges.

**Solution**

We set and we observe that

That’s all folks.