Sum of the series S=1+12(1+2)+13(1+2+3)+14(1+2+3+4)+…up to 20 terms is

Sum of the series S=1+12(1+2)+13(1+2+3)+14(1+2+3+4)+up to 20 terms is

  1. A

    110

  2. B

    111

  3. C

    115

  4. D

    116

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    Solution:

    Let tk denote the kth term of the series. Then

    tk=1k(1+2+3++k)=1kk(k+1)2=k+12.

    Thus, S=12[2+3+4++21]=102(2+21)=115

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