A question from Concrete Mathematics

[login]

I have a question when reading Concrete Mathematics.It's in Unit 2(SUMS) section 7(INFINITE SUMS).Authors have proved that ∑_k>=0x^k=1/(1-x) (0<=x<1), but they also say: We might also try setting x=-1 in the formula ∑_k>=0x^k=1/(1-x), since we've proved that this formula holds when 0<=x<1.(Maybe It's on Page 59) I don't know why they can set x=-1 and use the formula correctly. The formula is right when 0<=x<1, isn't it? (PS: My English is really poor. Please point out my mistakes. Thank you!)

Edited August 6, 2011 by login

[mathematic]

The formula is correct for |x| < 1 (or -1 < x < 1). The series does not converge for other values of x. If you are familiar with complex numbers, the condition |x| < 1 applies here also.

[login]

Thank you very much! Although I can't understand your words completely(Because of my poor mathematical level).

Edited August 7, 2011 by login