11th Class Mathematics Sample Paper Mathematics Olympiad - Sample Paper-4

  • question_answer 18) The A.M. of the series \[\mathbf{1},\mathbf{2},\mathbf{4},\mathbf{8},\mathbf{16}....{{\mathbf{2}}^{\mathbf{4}}}\]is

    A) \[\frac{{{2}^{n}}-1}{n}\]                    

    B) \[\frac{{{2}^{n+1}}-1}{n+1}\]      

    C) \[\frac{{{2}^{n}}+1}{n}\]                              

    D) \[\frac{{{2}^{n}}-1}{n+1}\]

    Correct Answer: A

    Solution :

    [a] \[{{S}_{n}}=\frac{a({{r}^{n}}-1)}{r-1}=\frac{1.({{2}^{n}}-1)}{2-1}={{2}^{n}}-1\] Arithmatic Mean\[=\frac{({{2}^{n}}-1)}{2-1}\] Hence, option [a] is correct.

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