Lemma

For [Maple Math] and a sequence of values [Maple Math] with

[Maple Math] and [Maple Math] for [Maple Math] ,

the following result holds:

[Maple Math]

>

This can be shown as follows:

For a fixed integer [Maple Math] , we get that

[Maple Math]

[Maple Math]

[Maple Math]

......

[Maple Math]

>

Since the second term above contains a geometric series with ratio [Maple Math] , and hence sum

[Maple Math] = [Maple Math] .

we find

[Maple Math] .

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Using the previous lemma we obtain the required inequality:

[Maple Math]

>