lim<n→∞>n[ln(n+1)-lnn]
=lim<n→∞>n*ln[(n+1)/n]
=lim<n→∞>ln[(n+1)/n]^n
=lim<n→∞>ln[1+(1/n)]^n
=lne
=1
lim<x→∞>[(x+2a)/(x-a)]^(x/3)=8
===> lim<x→∞>[(x-a+3a)/(x-a)]^(x/3)=8
===> lim<x→∞>[1+3a/(x-a)]^(x/3)=8
===> lim<x→∞>{[1+3a/(x-a)]^(x-a)/(3a)}^[ax/(x-a)]=8
===> e^lim<x→∞>[ax/(x-a)]=8
===> e^a=8
===> a=ln8=3ln2
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