Is it possible to this sequence?

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Homework Statement


given:

Vn+1=Vn*cos(pi/2^(n+2)) and Vn= pi/2


Homework Equations



Write Vn in terms of n

The Attempt at a Solution



how can i start this. I already know that -1<cosx<1 and I've already proved that this sequence is a negative sequence. Then our teacher said if its possible to write Vn in terms of n?
 
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Wrong attachement.
 

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correct attachment:
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Thread 'Finding the nth roots of a complex number'

There are two things I don't understand about this problem. First, when finding the nth root of a number, there should in theory be n solutions. However, the formula produces n+1 roots. Here is how. The first root is simply ##\left(r\right)^{\left(\frac{1}{n}\right)}##. Then you multiply this first root by n additional expressions given by the formula, as you go through k=0,1,...n-1. So you end up with n+1 roots, which cannot be correct. Let me illustrate what I mean. For this...
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