Explain why a power series is tested for absolute convergence.

Solution 4EExplain why a power series is tested for absolute convergence.Step 1:A power series about x=a is of the formTo test for the convergence of the series we will use a modified ratio test.It is given by The result of this test will be an absolute value of the form We will now determine where this expression is less than one. R is called the radius of convergence, and is the interval of convergence. The power series converges absolutely for any x in that interval.Therefore a power series is tested for absolute convergence