JEE Main & Advanced Mathematics Sequence & Series Question Bank Self Evaluation Test - Sequences and Series

  • question_answer
    Let a = 111... 1(55 digits), \[b=1+10+{{10}^{2}}+...+{{10}^{4}},\] \[c=1+{{10}^{5}}+{{10}^{10}}+{{10}^{15}}+....+{{10}^{50}},\]then

    A) \[a=b+c\]

    B) \[a=bc\]

    C) \[b=ac\]

    D) \[c=ab\]

    Correct Answer: B

    Solution :

    [b] \[a=1+10+{{10}^{2}}+....+{{10}^{54}}\] \[=\frac{{{10}^{55}}-1}{10-1}=\frac{{{10}^{55}}-1}{{{10}^{5}}-1}.\frac{{{10}^{5}}-1}{10-1}=bc\]


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