JEE Main & Advanced Mathematics Other Series Question Bank Critical Thinking

  • question_answer 16) \[1+\frac{2}{3}-\frac{2}{4}+\frac{2}{5}-......\infty =\]

    A) \[{{\log }_{e}}3\]

    B) \[{{\log }_{e}}4\]

    C) \[{{\log }_{e}}\left( \frac{e}{2} \right)\]

    D) \[{{\log }_{e}}\left( \frac{2}{3} \right)\]

    Correct Answer: B

    Solution :

    \[S=1+2\left\{ \frac{1}{3}-\frac{1}{4}+\frac{1}{5}-\frac{1}{6}+.... \right\}\] \[=\left( 2-\frac{2}{2} \right)+2\left\{ \frac{1}{3}-\frac{1}{4}+\frac{1}{5}-\frac{1}{6}+.... \right\}\] \[=2\left\{ 1-\frac{1}{2}+\frac{1}{3}-\frac{1}{4}+... \right\}=2{{\log }_{e}}2\] = \[{{\log }_{e}}4\].

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