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| Going Geometric With The Limit (Posted on 2008-03-26) |
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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.
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Submitted by K Sengupta
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Rating: 2.0000 (2 votes)
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Solution:
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(Hide)
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The required limit is 1/e.
For the bonus problem, the required limit is 27/(4*e)
EXPLANATION:
Refer to the solution submitted by Chesca Ciprian in
this location.
For an alternative methodology, refer to the solution submitted by Paul
in this location.
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