2. Questions Bank
  3. JEE Main & Advanced
  4. Mathematics
  5. Sequence & Series

JEE Main & Advanced Mathematics Sequence & Series Question Bank Arithmetico - Geometric Series, Method of difference

  • question_answer
    The sum of the series \[1+\frac{1.3}{6}+\frac{1.3.5}{6.8}+....\infty \]is [UPSEAT 2001]

    A) 1

    B) 0

    C) \[\infty \]

    D) 4

    Correct Answer: D

    Solution :

    Let, \[S=1+\frac{1.3}{6}+\frac{1.3.5}{6.8}+...\infty \] Þ \[\frac{S}{4}=\frac{1}{4}+\frac{1.3}{4.6}+\frac{1.3.5}{4.6.8}+....\infty \] Þ \[\frac{1}{2}-\frac{S}{8}=\frac{1}{2}-\frac{1}{2}.\frac{1}{4}-\frac{1}{2}.\frac{1.3}{4.6}-\frac{1}{2}\frac{1.3.5}{4.6.8}-....\infty \] Þ \[\frac{1}{2}-\frac{S}{8}=1-\frac{1}{2}+\frac{\frac{1}{2}\left( \frac{1}{2}-1 \right)}{1.2}-\]\[\frac{\frac{1}{2}\left( \frac{1}{2}-1 \right)\,\left( \frac{1}{2}-2 \right)}{1.2.3}\]\[+\frac{\frac{1}{2}\left( \frac{1}{2}-1 \right)\,\,\left( \frac{1}{2}-2 \right)\,\,\left( \frac{1}{2}-3 \right)}{1.2.3.4}....\infty \] Þ \[1/2-S/8={{(1-1)}^{1/2}}=0\] Þ \[S/8=1/2\Rightarrow S=4\].


You need to login to perform this action.
You will be redirected in 3 sec spinner