Determine the radius of convergence of the series ∑ n = 1 ∞ a n z n where a n = n 2 4 n + 3 n

Question

Determine the radius of convergence of the series       ∑          n      =      1              ∞            a    n        z    n   where       a    n    =            n      2                      4        n            +      3      n

grcalia1 · Accepted Answer

You have      a    n    =      4          −      n                  n      2              1      +      3      n              4                  −          n                      ,and therefore      lim          n      →      ∞                  a      n        n    =      lim          n      →      ∞            1    4                      n        2                    1        +        3        n                  4                      −            n                                n    =      lim          n      →      ∞            1    4                      n        n            2                      1        +        3        n                  4                      −            n                              n        =      1    4    .Therefore, the radius of convergence is 4

Determine the radius of convergence of the series ∑ n = 1 ∞ a n...

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