原式=lim{n->∞}{[1+(a^{1/n}+b^{1/n}-2)/2]^{1/(a^{1/n}+b^{1/n}-2)}}^{n/(a^{1/n}+b^{1/n}-2)}
=e^(lim{n->∞}{(a^{1/n}+b^{1/n}-2)/{1/n}})=e^(lim{n->∞}{(a^{1/n}-1)/{1/n}+(b^{1/n}-1)/{1/n}})
=e^{lna+lnb}=e^{lnab}=ab（ab）＾1／2原式=lim{n->∞}{[1+(a^{1/n}+b^{1/n}-2)/2]^{2/(a^{1/n}+b^{1/n}-2)}}^{n(a^{1/n}+b^{1/n}-2)/2}=e^(lim{n->∞}{½(a^{1/n}+b^{1/n}-2)/{1/n}})=e^(lim{n->∞}{½(a^{1/n}-1)/{1/n}+(b^{1/n}-1)/{1/n}})=e^{½(lna+lnb)}=e^{½lnab}=√ab