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!

Thanks!

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- Nov 8th 2010, 10:27 AMbubblygirl90Asymptotic expansion
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!

Thanks! - Nov 9th 2010, 03:34 AMbubblygirl90
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