[tex]1+x^{1}+x^{2}+...+x^{99}=\frac{x^{100}-1}{x-1}[/tex]
[tex]\frac{x^{100}-
1}{x-1}=0~<=>~x^{100}-1=0[/tex]
[tex]x^{100}-1=0~=>x^{100}=1~=>x=+-1[/tex]
Daca x diferit de 1, deci x=-1
Daca x=-1
1+x^1+x^2+...+x^99
=1+(-1)^1+(-1)^2+...+(-1)^99
=1+(-1)+1+(-1)+...+(-1)=
(se reduc toti 1 si -1)
=0
