I try to solve the following tricky limit: lim x → ∞ ∑ k = 1 ∞ k x ( k 2 + x ) 2

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I try to solve the following tricky limit:      lim          x      →      ∞            ∑          k      =      1              ∞                  k      x              (              k        2            +      x              )        2

iberistazi · Accepted Answer

Notice that, for fixed x, your sum is less than      ∫    0    ∞              k      x              (              k        2            +      x              )        2                d  k  =      1    2      ,and greater than      ∫    1    ∞              k      x              (              k        2            +      x              )        2                d  k  =      x          2      (      1      +      x      )          ,and then apply the squeeze theorem.

I try to solve the following tricky limit: <munder> <mo movablelimits="true" form="prefix">l

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