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

  • question_answer
    The sum of the series: \[1+\frac{3}{2}+\frac{5}{4}+\frac{7}{6}+......\infty \]is equal to

    A) 3e                    

    B) 2e             

    C) e                                  

    D) 5e

    Correct Answer: C

    Solution :

    [c]\[1+\frac{3}{2}+\frac{5}{4}+\frac{7}{6}+......to\,\,\infty \] \[=1+\frac{2+1}{2}+\frac{4+1}{4}+\frac{6+1}{6}+......to\,\,\infty \] \[=1+\frac{1}{1}+\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+\frac{1}{5}+\frac{1}{6}......to\,\infty ={{e}^{1}}=e\]Hence, option [c]is correct.


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