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Sum simplifying


Hey,

I'd like to simplify a following type of sum:

In[62]:= Sum[a[k]*I + b[k], {k, 1, n}] - I*Sum[a[k], {k, 1, n}] - 
 Sum[b[k], {k, 1, n}]

In[63]:= FullSimplify[%]

The result should obviously be zero; however, Mathematica returns the same expression. If I put n an integer value it knows how to simplify. How do I make it understand that also with a symbolic upper limit?

Hope someone can help!

Thanks,
Lari


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