Good old Limits
n → ∞ lim 2 1 ( n 2 n ) n 1 = ?
Notation: ( N M ) = N ! ( M − N ) ! M ! denotes the binomial coefficient .
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1 solution
And why is that 2?
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the limit will be 4 Since and half of it will be 2.
I added the 1/2 just so that people would do that mistake at the end lol.
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Still why is 2 l o g ( 2 ) = 2 ?
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@Peter van der Linden – 2log2 is not 2 . If you see that I said the limit equals e^L . where L=(after evaluating) 2log2. So the value equals 4 and then after dividing by 2 it becomes 2.
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@Arghyadeep Chatterjee – Still don't get it... Log isn't the same as ln, so e^(2log2) is still not 4.
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@Peter van der Linden – Ok sorry my bad . Actually everyone are used take log as ln if no information about the base is mentioned . It is not a good thing to do in algebra but I think it is safe to do in calculus. Anyways I should have clarified that in my solution. It is actually a common practise in India to take log as ln .
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@Arghyadeep Chatterjee – Aah then it's a translation problem! And I thought math was such a universal language. In Europe it's common to read base 10 if there's nothing mentioned as base.
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@Peter van der Linden – But anyways you should have figured it out that here log was to the base e when I raised the limit to the power of e.
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@Arghyadeep Chatterjee – Nope I just got confused... And couldn't manage to figure it out anymore.
@Arghyadeep Chatterjee – Yeah it's matter of common and natural log.