The value of limn→∞ 1⋅2+2⋅3+3⋅4+…+n(n+1)n3 ,is 

The value of limn12+23+34++n(n+1)n3 ,is 

  1. A

    1

  2. B

    -1

  3. C

    13

  4. D

    none of these 

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    Solution:

    We have, 

    limn12+23+34++n(n+1)n3=limnr=1nr(r+1)n3=limnr=1nr2+r=1nrn3=limnn(n+1)(2n+1)6+n(n+1)2n3=limnn(n+1)(n+2)3n3=13

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