高等数学 利用定积分的和式极限

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L =lim(n->兆告∞改猜知核消) (1/n)[ n(n+1)...(2n-1) ]^(1/n)
=lim(n->∞) [ (1+1/n)(1+2/n)...(1+(n-1)/n) ]^(1/n)
lnL =lim(n->∞) (1/n) ∑(i:1->n-1) ln(1+i/n)
=lim(n->∞) (1/n) ∑(i:1->n) ln(1+i/n)
= ∫(0->1) ln(1+x) dx
= [x.ln(1+x)]|(0->1) - ∫(0->1) x/(1+x) dx
=-∫(0->1) [1-1/(1+x)] dx
= -[x- ln|1+x|]|(0->1)
= ln2 -1
L =e^(ln2-1)
= 2/e

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