Page:Elements of the Differential and Integral Calculus - Granville - Revised.djvu/249



Substituting $$x = 1$$ in (B), we get

which is an alternating series that converges.

Substituting $$x = -1$$ in (B), we get

which is convergent by comparison with the p series ($$p>l$$). The series in the above example is said to have $$[-1, 1]$$ as the interval of convergence. This may be written $$-1 \le x \le 1$$, or indicated graphically as follows:



For what values of the variable are the following series convergent?