login Posted August 6, 2011 Share Posted August 6, 2011 (edited) I have a question when reading Concrete Mathematics.It's in Unit 2(SUMS) section 7(INFINITE SUMS).Authors have proved that ∑k>=0xk=1/(1-x) (0<=x<1), but they also say: We might also try setting x=-1 in the formula ∑k>=0xk=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 Link to comment Share on other sites More sharing options...
mathematic Posted August 6, 2011 Share Posted August 6, 2011 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. Link to comment Share on other sites More sharing options...
login Posted August 7, 2011 Author Share Posted August 7, 2011 (edited) Thank you very much! Although I can't understand your words completely(Because of my poor mathematical level). Edited August 7, 2011 by login Link to comment Share on other sites More sharing options...
Recommended Posts
Create an account or sign in to comment
You need to be a member in order to leave a comment
Create an account
Sign up for a new account in our community. It's easy!
Register a new accountSign in
Already have an account? Sign in here.
Sign In Now