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# Limits Watch

1. I can't seem to be able to figure out this limit:
lim(1-1/n)^n as n -> infinity. When i stick values into the calculator i can see that it tends to 1/e but is there a nice way to work this one out? Thanks!
2. (Original post by JBKProductions)
I can't seem to be able to figure out this limit:
lim(1-1/n)^n as n -> infinity. When i stick values into the calculator i can see that it tends to 1/e but is there a nice way to work this one out? Thanks!
I can't see a nicer way to evaluate this limit without using L'Hôpital's rule. Start off by taking the natural log of the limit and manipulate the expression until the numerator consists of a single term, which is a logarithm. Then apply L'Hôpital's rule.
It's a very famous definition.
3. there might be an easier way:
but if you
let y=(1-1/n)^n
lny=nln(1-1/n)

then use maclaurian series to expand ln(1-1/n) and evaluate
4. (Original post by Farhan.Hanif93)
It doesn't tend to 1/e.
It does, check the sign. In general . Using L'Hôpital's rule is probably fine... but then you're not allowed to use it as a definition of the exponential function. (That would be circular.)
5. (Original post by Zhen Lin)
It does, check the sign. In general . Using L'Hôpital's rule is probably fine... but then you're not allowed to use it as a definition of the exponential function. (That would be circular.)
This is why I shouldn't be doing maths at this time, sign errors all over the place.

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