Evaluate:

Limit T(m)/m
m → ∞

where, T(m) is the geometric mean of m positive integers 1, 2, ..., m.

Bonus Problem

As a bonus, work out the following limit:

Limit U(m)/m
m → ∞

where, U(m) is the geometric mean of m positive integers 2m+1, 2m+2, ..., 3m.

Taking a huge number of terms for the first part, the solution looks suspiciously like 1/e. but I can't rigorously prove it...

Posted by Kenny M on 2008-03-26 20:55:46