2. Questions Bank
  3. JEE Main & Advanced
  4. Mathematics
  5. Binomial Theorem and Mathematical Induction

JEE Main & Advanced Mathematics Binomial Theorem and Mathematical Induction Question Bank Self Evaluation Test - Binomial Theorem

  • question_answer
    If \[y=3x+6{{x}^{2}}+10{{x}^{3}}+........\infty \], then\[\frac{1}{3}y-\frac{1.4}{{{3}^{2}}2}{{y}^{2}}+\frac{1.4.7}{{{3}^{2}}3}{{y}^{3}}-.....\,\infty \] is equal to

    A) x

    B) \[1-x\]

    C) \[1 + x\]

    D) \[{{x}^{x}}\]

    Correct Answer: A

    Solution :

    [a] We have \[y=3x+6{{x}^{2}}+10{{x}^{3}}+......\] \[\Rightarrow 1+y=1+3x+6{{x}^{2}}+10{{x}^{3}}+.....\] \[\Rightarrow 1+y={{(1-x)}^{-3}}\Rightarrow 1-x={{(1+y)}^{-1/3}}\] \[\Rightarrow x=1-{{(1+y)}^{-1/3}}\] \[=\frac{1}{3}y-\frac{1.4}{{{3}^{2}}.2}{{y}^{2}}+\frac{1.4.7}{{{3}^{2}}.3}{{y}^{3}}-........\]


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