Evaluate the limit

**Solution**

One may use creative telescoping and deduce the double inequality

since . The limit follows to be .

Another way is using Riemann sum. Note that

*Choose which one you prefer the most. *

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# A zeta tail limit

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Evaluate the limit

**Solution**

One may use creative telescoping and deduce the double inequality

since . The limit follows to be .

Another way is using Riemann sum. Note that

*Choose which one you prefer the most. *