title: rolling mean with increasing window
body: <p>I have a range</p>
  
  <pre><code>np.arange(1,11) # [1, 2, 3, 4, 5, 6, 7, 8, 9, 10]
  </code></pre>
  
  <p>and for each element, <em>i</em>, in my range I want to compute the average from element <em>i=0</em> to my current element. the result would be something like:</p>
  
  <pre><code>array([ 1. ,  1.5,  2. ,  2.5,  3. ,  3.5,  4. ,  4.5,  5. ,  5.5])
   # got this result via np.cumsum(np.arange(1,11,dtype=np.float32))/(np.arange(1, 11))
  </code></pre>
  
  <p>I was wondering if there isn't an out of the box function in numpy / pandas that gives me this result?</p>