title: Join Series on MultiIndex in pandas
body: <p>I have multiple Series with a MultiIndex and I'd like to combine them into a single DataFrame which joins them on the common index names (and broadcasts values). The setup is like</p>
  
  <pre><code>import pandas as pd
  a=pd.Series([12,13,14,15], index=pd.MultiIndex.from_tuples([(1,1),(1,2),(2,1),(2,2)], names=["i", "j"]))
  b=pd.Series([21,22], index=pd.MultiIndex.from_tuples([(1,),(2,)], names=["i"]))
  </code></pre>
  
  <p>How can I get the result</p>
  
  <pre><code>i  j  a  b
  1  1  12 21 
  1  2  13 21
  2  1  14 22
  2  2  15 22
  </code></pre>
  
  <p>Can you suggest how to get this result? Ideally this should also work on more than two Series.</p>