JEE Main & Advanced Mathematics Binomial Theorem and Mathematical Induction Question Bank Mock Test - Principle of Mathematical Induction

  • question_answer
    The sum of the series \[\frac{2}{3}+\frac{8}{9}+\frac{26}{27}+\frac{80}{81}+.....\]to n terms is

    A) \[n-\frac{1}{2}(1-{{3}^{-n}})\]

    B) \[n-\frac{1}{2}({{3}^{-n}}-1)\]

    C) \[n-\frac{1}{2}({{3}^{n}}-1)\] 

    D) \[n+\frac{1}{2}({{3}^{n}}-1)\]

    Correct Answer: A

    Solution :

    [a] Assigning values to n, we get the answer.


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