- #1
Robin04
- 260
- 16
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/Recur...currence_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?