Problem of the month for September 2008

From the current issue of Mathematics Magazine.
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For nonnegative  a, b,  and  c,  find the limit of

sum(k=1..n,  sqrt(n^2 + kn + a) / [sqrt(n^2 + kn + b) sqrt(n^2 + kn + c)])

as  n  grows arbitrarily large.
</pre>