At first glance , I though that the series ∑ n = 0 ∞ ( − z ) n

Question

At first glance , I though that the series      ∑          n      =      0              ∞        (  −  z      )    n

EreneDreaceaw · Accepted Answer

Write your power series as      ∑          n      =      0        ∞        (    −    1          )      n              z      n        .By the Cauchy–Hadamard formula the radius of convergence R is  R  =      1                            lim          sup                          n          →          +          ∞                    ⁡                        |                      (            −            1                          )              n                                |                          1                      /                    n                      =      1                            lim          sup                          n          →          +          ∞                    ⁡              1                  1                      /                    n                      =      1                            lim          sup                          n          →          +          ∞                    ⁡      1        =      1    1    =  1.Thus, the power series converges if       |    z      |    &amp;lt;  1 and diverges if       |    z      |    &amp;gt;  1

At first glance , I though that the series <munderover> ∑ <mrow class="

Answered question

Answer & Explanation

New Questions in Calculus 1