The value of lim from limx→∞ a11/x+a21/x+…+an1/xnnx, is

Let x=1y. Then,    limx→∞ a11/x+a21/x+…+an1/xnnx=limy→0 a1y+a2y+….+anynn/y=limy→0 1+a1y+a2y+….+any−nnn/y=limy→0 1+a1y−1+a2y−1+….+an1y−1nn/y=elimy→0a1y−1y+a2y−1y+….+any−1y=elog⁡a1+log⁡a2+i…+log⁡an=elog⁡a1a2−an=a1a2a3…an