Question #9f2d8

1 Answer
Alberto P.
Nov 14, 2016

#n(n-1)/2(a^n-2)#

Explanation:

#lim_(n->a)((x-a)(x^(n-1)+ax^(n-2)+...+a^(n-2)x+a^(n-1))-na^(n-1)(x-a))/(x-a)^2#

#lim_(n->a)((x^(n-1)+ax^(n-2)+...+a^(n-2)x+a^(n-1))-na^(n-1))/(x-a)#

#lim_(n->a)((x^(n-1)-a^(n-1))+a(x^(n-2)-a^(n-2))+...+a^(n-2)(x-a)+(a^(n-1)-a^(n-1)))/(x-a)#

#lim_(n->a)(x^(n-2)+...+a^(n-2))+a(x^(n-3)+...+a^(n-3))+...+a^(n-2)#

#=(n-1)a^(n-2)+a(n-2)a^(n-3)+...+a^(n-2)=#

#=a^(n-2)(n-1+n-2+....+1)=n(n-1)/2a^(n-2)#

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