若數(shù)列an=(1+1/n)^n,求證an
若數(shù)列an=(1+1/n)^n,求證an
數(shù)學(xué)人氣：280 ℃時(shí)間：2020-06-06 16:02:40
優(yōu)質(zhì)解答
a_(n+1) = ( 1 + 1/(n+1) ) ^ (n+1)= ( 1/n + 1/n + ...+ 1/n + 1/(n+1) ) ^ (n+1)> [ (n+1) ( 1/((n^n*(n+1)) )開(n+1)次方根 ] ^ (n+1) (均值不等式)= (n+1)^(n+1) * 1/((n^n)*(n+1))= (n+1)^n / n^n= ( (n+1)/n )...請(qǐng)問如何從第二行到第三行的？具體怎么用的均值不等式，我看不太懂……
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