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.

(In reply to not 100% rigorous solution by Paul)

Thanks Paul.

I confirm having hyperlinked your methodology in my solution.

Posted by K Sengupta on 2008-04-06 12:29:28