Question

prove that lim x->1 [m/(1-x^m)]-[n/(1-x^n]=(m-n)/2

Answer 1

I guess the best way L'Hopital's Rule after you manipulate the function a little bit

Answer 2

I know this problem solve with L'Hopital's Rule, but i want a proof.

Answer 3

you could put in this form
[m(1 - x^n) - n(1 - x^m)] / [(1-x^m)(1-x^n)]

Answer 4

and then take the derivative one time and then take it again and then evaluate and you will get the answer

Answer 5

thank you, but I want solve this problem without L'Hopital's Rule.

Answer 6

well then I suggest that you expand the expressions which would be a pain