Even-odd series
===============

A mathematical sequence is defined as:

:math:`x_1 = 0.1`

:math:`x_{i} = \begin{cases} 
x_{i-1} + 0.1 , & \mbox{if }   i-1    \mbox{ is even}  \\
x_{i-1} + 0.2 , & \mbox{if } i-1 \mbox{ is odd} \\ 
\end{cases}`

Write the function :py:func:`evenodd` that given a value
``v`` and a tolerance ``epsilon``, returns the number of terms of the
sequence, beginning from :math:`x_1`, which must be added to get
the exact value ``v`` with a tolerance ``epsilon``.  In case the sum of
terms never gives this value with this precision, the function will
return -1. Keep in mind that it is a increasing series.

For example, for ``v= 1.4`` the function will return ``4``, because the sum of the 4 first terms of the sequence (0.1+0.3+0.4+0.6) is exactly 1.4:

.. math::
   \begin{array}{l}
   x_1 = 0.1 \\
   x_2 = x_1 + 0.2 = 0.1 + 0.2 = 0.3 \\  
   x_3 = x_2 + 0.1 = 0.3 + 0.1 = 0.4 \\
   x_4 = x_3 + 0.2 = 0.4 + 0.2 = 0.6 \\
   \end{array}


Save the function into file ``series.py``. Examples:
   
   .. literalinclude:: even-odd.txt
      :language: python3
      :lines: 3-
             
   .. note::

      You can download the file with tests :download:`even-odd.txt <even-odd.txt>`

.. rubric:: Solution
      
A solution of these functions is provided in the :download:`series.py
<solutions/series.py>`