求lim(x趋向于1)(x+x^2+x^3+...+x^n-n)/(x-1)

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求lim(x趋向于1)(x+x^2+x^3+...+x^n-n)/(x-1)求lim(x趋向于1)(x+x^2+x^3+...+x^n-n)/(x-1)求lim(x趋向于1)(x+x^2+x^3+..

求lim(x趋向于1)(x+x^2+x^3+...+x^n-n)/(x-1)
求lim(x趋向于1)(x+x^2+x^3+...+x^n-n)/(x-1)

求lim(x趋向于1)(x+x^2+x^3+...+x^n-n)/(x-1)
由洛必达法则,
lim(x趋向于1)(x+x^2+x^3+...+x^n-n)/(x-1)
=lim(x趋向于1)(x+x^2+x^3+...+x^n-n)'/(x-1)'
=lim(x趋向于1)(1+2x+3x^2+nx^(n-1)-n)/1
=1+2+3+4+...+n-1
=n(n-1)/2