x→1时lim(x+x2+.+xn-n)/(x-1) 的极限值
题目
x→1时lim(x+x2+.+xn-n)/(x-1) 的极限值
答案
lim(x→1) (x+x2+.+xn-n)/(x-1)= lim(x→1) [x^(n+1)-x-n(x-1)]/(x-1)^2 (0/0型,运用洛必达法则)= lim(x→1)1/2* [(n+1)x^n-1-n]/(x-1) (0/0型,运用洛必达法则)=lim(x→1)1/2* n(n+1)x^(n-1)=n(n+1)/2...
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