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## Homework Statement

Prove harmonic series is divergent by comparing it with this series.

##\frac{1}{1}+\frac{1}{2}+(\frac{1}{4}+\frac{1}{4})+(...)##

## The Attempt at a Solution

Clearly every term in harmonic series is equal or larger than the term in the second series ##n \geq 1##, hence like the second series the harmonic series must be divergent. The second series denominator has the form ##2^k##. For any integer ##k##, ##\frac{1}{n} \geq \frac{1}{2^k}##

Is this proof good enough? If not how do I formalize the proof more? What needs to be shown in this case?