Solutions:

**dr Sonnhard Graubner**

. The searched limit is .

**fredoniahead**

Look at the identity:

, remembering that . Let

**JoeBlow **

It’s equal to:

.

**WWW**

Another approach: Apply to get . Now for , so the last sum lies between and This (Cesaro-Stolz or the well known fact that ). Thus the original limit is

**Indeed,from the very definition, as JoeBlow mentioned. What about the following?**

R-limit = , where is prime for .

I already received one answer, but haven’t analyzed it for correctness yet. Shown below.

**Xantos C. Guin**

Let and .

Clearly, for all . Also, for all integers .

Hence, , and thus, as well.

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