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**zahlenspieler****Member**- Registered: 2018-04-12
- Posts: 7

Hi everyone!

It all started when I proved

Let ,

where

Now I would like to show that ,

where .

So I proved the following inequality for positive integers :

.

Expanding

gives.

As n grows towards infinity, the binomial coefficients go to . Now taking the absolute values, that sequence is bounded above by .

But now I got stuck. One idea that I have is the sandwich theorem -- i.e. to 'squeeze' the sequence of partial sums of the cosine series between that sequence above and another sequence

The trouble is the altering signs, so I just can't add up inequalities ...

Any ideas?

Regards,

zahlenspieler

*Last edited by zahlenspieler (2018-04-19 17:10:29)*

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