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# A limit!

Evaluate the limit:

Solution

Let . Then,

It follows by Stolz–Cesàro that

Hence .

## 1 Comment

1. Oliver says:

We can also invoke another technique; that of the double summation.

First of all , we note that

Hence,

The last line follows from the fact that . Thus,

However, justifying this convergence requires more than the usual Riemann sum argument. 🙂

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