Does this converge or diverge? ∑ n = 1 ∞ ( a n = 1 2 n + n 3 )

Question

Does this converge or diverge?      ∑          n      =      1        ∞    (      a          n        =      1          2              n            +              n        3              )

Cristian Hamilton · Accepted Answer

n              2              n            +              n        3              =            n                      n                    (        2        +                              n            3                                n                          )              =      1          2      +                        n          3                          n                      →      1    2    ,       as           n      →      ∞      because            n      3              n        =      n          1              /            3            /        n          1              /            2        =      n          1              /            3      −      1              /            2        =      n          −      1              /            6      An other argument goes like this      n    3    ≤      n    ,so that  2      n    +      n    3    ≤  3      n  and then            n              2              n            +              n        3              ≥            n              3              n              &amp;gt;  1      /    5

Does this converge or diverge? <munderover> <mo movablelimits="false">∑

Answered question

Answer & Explanation

New Questions in Calculus 2