dr Sonnhard Graubner
Look at the identity:
, remembering that . Let
It’s equal to:
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.