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Sorry if this is an easy one- I've tried everything I can think of (which isn't much), but hopefully there's an easy answer I'm not getting.

I'd like to show that $$\lim_{n\to \infty} \prod_{k=1}^n \left(1+\frac an + \frac {bk}{n^2}\right) = e^{a + b/2}.$$ Wolfram Alpha says it's true (for particular values of a and b), but doesn't say why. I guess you could expand the product by hand and just look at the part that's constant in $n$, but this immediately gets very complicated and I'm not used to making counts like that. Any other ideas? Thanks a lot-

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    Take the logarithm of both sides and use Taylor series.2011-07-25

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