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 Gauss-D'Alemebert by Chesca Ciprian)

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Edited on April 12, 2008, 4:19 pm

Posted by K Sengupta on 2008-04-06 12:32:26