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JEE Main & Advanced Sample Paper JEE Main Sample Paper-12

  • question_answer
    The sum to infinity of the series \[\frac{1}{1}+\frac{1}{1+2}+\] \[\frac{1}{1+2+3}+\frac{1}{1+2+3+4}+......,\] is equal to

    A)  3                                            

    B)  1

    C)  2                                            

    D)  3/2

    Correct Answer: C

    Solution :

     \[\frac{1}{1}+\frac{1}{1+2}+\frac{1}{1+2+3}+\frac{1}{1+2+3+4}+\]?? \[{{t}_{n}}=\frac{1}{1+2+3+......n}=\frac{1}{n(n+1)}=2\left[ \frac{1}{n}-\frac{1}{n+1} \right]\] \[\therefore \]Sum \[=S=2\left[ \left( \frac{1}{1}-\frac{1}{2} \right)+\left( \frac{1}{2}-\frac{1}{3} \right)+\left( \frac{1}{3}-\frac{1}{4} \right)+......... \right]\]=2


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