原式=lim(n->∞){4[(1+(1+2^n+3^n)/4^n)^(4^n/(1+2^n+3^n))]^[(1/n)(1+2^n+3^n)/4^n]}
=4e^{lim(n->∞)[(1/n)(1+2^n+3^n)/4^n]} (應(yīng)用重要極限lim(z->0)[(1+z)^(1/z)]=e)
=4e^{lim(n->∞)[(1/n)((1/4)^n+(2/4)^n+(3/4)^n)]}
=4e^[0*(0+0+0)]
=4.
跪求函數(shù)的極限：lim(1^n+2^n+3^n+4^n)^1/n,當(dāng)n→∞時(shí)的極限.(不用夾逼準(zhǔn)則解)
跪求函數(shù)的極限：lim(1^n+2^n+3^n+4^n)^1/n,當(dāng)n→∞時(shí)的極限.(不用夾逼準(zhǔn)則解)
數(shù)學(xué)人氣：403 ℃時(shí)間：2020-05-09 20:52:20
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