limn→∞ an+bn2n,a,b>0 equals

limnan+bn2n,a,b>0 equals

  1. A

    1

  2. B

    ab

  3. C

    ab

  4. D

    2b2

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    Solution:

         limnan+bn2n

    =limn1+a1/n+b1/n22n

    =limn1+a1/n1+b1/n12n

    =elimn na1/n-1+b1/n-12

    =e12limna1/n11/n+b1/n1/n1=e1logea+logeb=elogeab=ab.

     

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