Question

lim(x的N次方-1/X的M次方-1)等于多少

Answer 1

因式分解 x^N -1 = (x-1) * [ x^(N-1) + x^(N-2) + .+x + 1 ]

x^M -1 = (x-1) * [ x^(M-1) + x^(M-2) + .+x + 1 ]

原式 = lim [ x^(N-1) + x^(N-2) + .+x + 1] / [ x^(M-1) + x^(M-2) + .+x + 1] ,x->1]

= N / M