anonymous
  • anonymous
Why \(lim_{n \to \infty}(1-\frac{1}{n})^{n} = e^{-1} \) ? OR How can i find this rule, whats it name ?
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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schrodinger
  • schrodinger
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anonymous
  • anonymous
I thought it should be \[\lim{n \to \infty}(1-0)^{n}\]
anonymous
  • anonymous
hiii, binomial expansion of \[(1+x)^{n}\] substitute for n=1/x you'll get binomial expansion as : \[(1+x)^{1/x}\] = 1+ x*1/x + (1-x)/2! + (1-x)(1-2x)/3!+............ now apply limit x tending to 0 you'll get : 1+1+1/2!+ 1/3!+.......... = e similarly for \[(1-x)^{x}\] we get e-1 :)
anonymous
  • anonymous
can we find this rule in internet, is it possible to send a link for it ?

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anonymous
  • anonymous
yeah you can google that out !! I answerd that on what I recently studied :)
anonymous
  • anonymous
ok i think your answer is good enough, but to understand better i need to read once more i think from other source..
anonymous
  • anonymous
what is this number name \[e^{-1}\] ?
anonymous
  • anonymous
it's actually exponential to the power -1... we write it as " e " it's value approximately equals to 2.7
anonymous
  • anonymous
ok..
anonymous
  • anonymous
e-1 = 1/e is it more clear now..?
anonymous
  • anonymous
ok thank you very much, its clearer
anonymous
  • anonymous
we can expand e^x as 1+ x/1! + x^2/2! + x^3/3!+......
anonymous
  • anonymous
hmm...
anonymous
  • anonymous
ok thank you meera now its much clearer, thanks for your efforts
anonymous
  • anonymous
:)

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