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=limn²(e^((n+1)ln(1+1/(n+1)))-e^(nln(1+1/n)))
=limn²(e^((n+1)ln(1+1/(n+1))-nln(1+1/n))-1)*lime^(nln(1+1/n)
=elimn²((n+1)ln(1+1/(n+1))-nln(1+1/n))
=elim((1/u+1)ln(1+1/(1/u+1))-ln(1+u)/u)/u²
=elim((1+u)(ln(1+2u)-ln(1+u))-ln(1+u))/u³
=elim(ln(1+2u)-ln(1+u)+(1+u)(2/(1+2u)-1/(1+u))-1/(1+u))/3u²
=elim(ln(1+2u)-ln(1+u)+1/(1+2u)-1/(1+u))/3u²
=elim(2/(1+2u)-1/(1+u)-2/(1+2u)²+1/(1+u)²)/6u
=elim(4u/(1+2u)²-u/(1+u)²)/6u
=e(4-1)/6
=e/2
=limn²(e^((n+1)ln(1+1/(n+1))-nln(1+1/n))-1)*lime^(nln(1+1/n)
=elimn²((n+1)ln(1+1/(n+1))-nln(1+1/n))
=elim((1/u+1)ln(1+1/(1/u+1))-ln(1+u)/u)/u²
=elim((1+u)(ln(1+2u)-ln(1+u))-ln(1+u))/u³
=elim(ln(1+2u)-ln(1+u)+(1+u)(2/(1+2u)-1/(1+u))-1/(1+u))/3u²
=elim(ln(1+2u)-ln(1+u)+1/(1+2u)-1/(1+u))/3u²
=elim(2/(1+2u)-1/(1+u)-2/(1+2u)²+1/(1+u)²)/6u
=elim(4u/(1+2u)²-u/(1+u)²)/6u
=e(4-1)/6
=e/2
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