Could somebody help me to see how to evaluate an integral from 0 to infinity of
(e^-t)*(1 + t/x)^-x as x goes to infinity
I know the answer is 1/2 + 1/8x - 1/32x^2 etc etc
Just not sure how to get to that point!
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Can anyone help with this? I've tried integrating by parts and expanding the bit in the brackets using binomial expansion but it hasn't really got me anywhere
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