Prove that the sequence is not bounded above
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January 15th 2012, 12:14 PM
alexmahone
Prove that the sequence is not bounded above
Prove that
is not bounded above.
January 15th 2012, 12:42 PM
girdav
Re: Prove that the sequence is not bounded above
We use
for
to get
.
Since
and
, we get the result.
}{2\cdot 4\cdots(2n)})
is not bounded above.\geq x-\frac{x^2}2)
for 
to get \geq \sum_{j=1}^n\frac 1{2j}-\frac 12\sum_{j=1}^n\frac 1{(2j)^2}=\frac 12\sum_{j=1}^n\frac 1j-\frac 18\sum_{j=1}^n\frac 1{j^2})
. 
and 
, we get the result.