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lep11
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Homework Statement
Prove that
a.) (1-(1/n2))n > 1- 1/n
b.) (1+ 1/(n-1))n-1 < (1 + 1/n)n
when n=2,3,4,5,...
Homework Equations
[/B]Bernoulli's inequality
(1+x)n ≥ 1+nx,
when x ≥-1 and n=2,3,4,5,...
(1+x)n >1+nx,
when x ≥-1, x≠0 and n=2,3,4,5,..
The Attempt at a Solution
a.)[/B] I applied Bernoulli's inequality.
First I checked 'the requirements'.
-1/n2 > -1 because n=1,2,3,... and -1/n2 ≠ 0 OK
Then (1-(1/n2))n > 1+ (- 1/n2)*n=1- 1/n Ok, done.
b.) I think I am supposed to apply Bernoulli's inequality as in part a, but don't have an idea how to get started.
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