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## Homework Statement

I need to find the explicit formula for the following recursive sequence:

##v_n=\frac{2}{1+q^n}v_{n-1}## where ##0<q<1## is a constant

## Homework Equations

I found the following method to solve it:

https://en.wikipedia.org/wiki/Recurrence_relation#Solving_first-order_non-homogeneous_recurrence_relations_with_variable_coefficients

## The Attempt at a Solution

Referring to Wikipedia, first I need to find

My sequence is homogenous so ##g_n = 0##

I'm already in a problem at the beginning. In order to find ##A_n## I need to calculate##\prod_{k=0}^{n-1} \frac{2}{1+q^k} = 2^{n-1}\prod_{k=0}^{n-1} \frac{1}{1+q^k}##

I don't really have any idea how to do this. Can you give me some hint?