求极限 Lim x→1(X^n-1)/(X-1)

问题描述:

求极限 Lim x→1(X^n-1)/(X-1)

lim (X^n-1)/(X-1)
= lim [ x^(n-1) + x^(n-2) + ...+ 1 ]
= ∑ lim x^k (k=1~n-1,共n-1项,为有限项,可展开)
= n-1