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Why \(lim_{n \to \infty}(1\frac{1}{n})^{n} = e^{1} \) ?
OR How can i find this rule, whats it name ?
 one year ago
 one year ago
Why \(lim_{n \to \infty}(1\frac{1}{n})^{n} = e^{1} \) ? OR How can i find this rule, whats it name ?
 one year ago
 one year ago

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tunahanBest ResponseYou've already chosen the best response.0
I thought it should be \[\lim{n \to \infty}(10)^{n}\]
 one year ago

meera_yadavBest ResponseYou've already chosen the best response.4
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 + (1x)/2! + (1x)(12x)/3!+............ now apply limit x tending to 0 you'll get : 1+1+1/2!+ 1/3!+.......... = e similarly for \[(1x)^{x}\] we get e1 :)
 one year ago

tunahanBest ResponseYou've already chosen the best response.0
can we find this rule in internet, is it possible to send a link for it ?
 one year ago

meera_yadavBest ResponseYou've already chosen the best response.4
yeah you can google that out !! I answerd that on what I recently studied :)
 one year ago

tunahanBest ResponseYou've already chosen the best response.0
ok i think your answer is good enough, but to understand better i need to read once more i think from other source..
 one year ago

tunahanBest ResponseYou've already chosen the best response.0
what is this number name \[e^{1}\] ?
 one year ago

meera_yadavBest ResponseYou've already chosen the best response.4
it's actually exponential to the power 1... we write it as " e " it's value approximately equals to 2.7
 one year ago

meera_yadavBest ResponseYou've already chosen the best response.4
e1 = 1/e is it more clear now..?
 one year ago

tunahanBest ResponseYou've already chosen the best response.0
ok thank you very much, its clearer
 one year ago

meera_yadavBest ResponseYou've already chosen the best response.4
we can expand e^x as 1+ x/1! + x^2/2! + x^3/3!+......
 one year ago

tunahanBest ResponseYou've already chosen the best response.0
ok thank you meera now its much clearer, thanks for your efforts
 one year ago
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