limx→∞ 121−x3+31+x2+521−x3+71+x2+… equals 

limx121x3+31+x2+521x3+71+x2+ equals 

  1. A

    56

  2. B

    103

  3. C

    56

  4. D

    none of these 

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    Solution:

    We have,

    limx121x3+31+x2+521x3+71+x2+=limx12+52+92+1x3+3+7+11+1+x2=limxk=1x(4k3)21x3+k=1x(4k-1)1+x2=limx16k=1xk224k=1xk+k=1x91x3+2x(x+1)x1+x2limx16x(x+1)(2x+1)12x(x+1)+9x1x3=326+2=103

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