Series 4
========

Consider the following mathematical succession:

    :math:`x_0 = 7`
    
    :math:`x_1 = 3`
    
    :math:`x_{n+1} = \frac{2*x_n+x_{n-1}}{3}`

It is well know that this succession converges to 4.0.

Implement the following Python function in the :mod:`series4` module (file :file:`series4.py`):

    .. py:function:: series4(eps, r)

such that *given*

    - `eps`, a :class:`float` such that `0 < eps < 1`.
    - `r`, an :class:`int`

    **returns** the list of all terms of the succession that are more than `eps` apart from 4.0. The terms to be included in the list must be rounded to ``r`` decimals (notice that the rounding should always be done after the comparison).

Desa la funció al fitxer ``series4.py`` i puja'l a Atenea. Els següents doctests mostren exemples del que ha de fer la funció:

For exemple:

   .. literalinclude:: series4-test.txt
      :language: python3
      :lines: 3-8

Doctests are available at the :download:`series4-test.txt <series4-test.txt>` file.