Home
Class 12
MATHS
Prove that following C(0)+(3)/(2).C(1)...

Prove that following
`C_(0)+(3)/(2).C_(1)+(9)/(3).C_(2)+(27)/(4).C_(3)+……+(3^(n))/(n+1).C_(n)=(4^(n+1)-1)/(3(n+1)).`

Promotional Banner

Topper's Solved these Questions

  • BINOMIAL THEOREM

    AAKASH SERIES|Exercise ADDITIONAL SOLVED EXAMPLES|10 Videos

  • BINOMIAL THEOREM

    AAKASH SERIES|Exercise EXERCISE - 3.1 (VERY SHORT ANSWER QUESTIONS)|44 Videos

  • BINOMIAL THEOREM

    AAKASH SERIES|Exercise EXERCISE - 1.4 (Level-2) |36 Videos

  • AREAS

    AAKASH SERIES|Exercise Exercise-3.2|21 Videos

  • CIRCLE

    AAKASH SERIES|Exercise EXERCISE -1.4|38 Videos

Similar Questions

Explore conceptually related problems

Prove that following (C_(1))/(2)+(C_(3))/(4)+(C_(5))/(6)+(C_(7))/(8)+……=(2^(n)-1)/(n+1)

Prove that following C_(0)+2.C_(1)+4.C_(2)+8.C_(3)+…+2^(n).C_(n)=3^(n)

Prove the following: C_(0)-(C_(1))/(2)+(C_(2))/(3) - …+(-1)^(n)(C_(n))/(n+1)=(1)/(n+1)

Prove that : If n is a positive integer and x is any nonzero real number, then prove that C_(0)+C_(1)(x)/(2)+C_(2).(x^(2))/(3)+C_(3).(x^(3))/(4)+….+C_(n).(x^(n))/(n+1)=((1+x)^(n+1)-1)/((n+1)x)

Prove that following i) 2.C_(0)+5.C_(1)+8.C_(2)+…..+(3n+2)C_(n)=(3n+4).2^(n-1)

Prove the following: C_(0)+(C_(2))/(3) +(C_(4))/(5) + … = (2^(n))/(n+1)

Prove the following: 1.2.C_(1)+2.3C_(2)+3.4.C_(3)+….n(n+1).C_(n) = n.(n+3).2^(n-2)

Prove the following: 2*C_(0)+3*C_(1)+4*C_(2)+…+(n+2)*C_(n)=(n+4).2^(n-1)

Prove the following: C_(0)+2*C_(1)_+3*C_(2)+…(n+1)*C_(n)=(n+2).2^(n-1)

Prove that 3.C_(0)^(2)+7.C_(1)^(2)+11.C_(2)^(2)+…..+(4n+3).C_(n)^(2)=(2n+3).""^(2n)C_(n).

AAKASH SERIES-BINOMIAL THEOREM-SOLVED EXAMPLES
  1. Prove that (C0 + C1) (C1 + C2) …..(C(n-1) + Cn) = ((n+1)^n)/(n!) (C1.C...

    Text Solution

    |

  2. Prove that sum(r = 1)^n r^3 ((Cr)/(C(r - 1))^2) = (n (n + 1)^2 (n+2))/...

    Text Solution

    |

  3. Prove that following C(0)+(3)/(2).C(1)+(9)/(3).C(2)+(27)/(4).C(3)+……...

    Text Solution

    |

  4. Find the range of x for which the binomial expansion of the following ...

    Text Solution

    |

  5. Find the range of x for which the binomial expansion of the following ...

    Text Solution

    |

  6. Find the range of x for which the binomial expansion of the following ...

    Text Solution

    |

  7. Find the range of x for which the binomial expansion of the following ...

    Text Solution

    |

  8. Find the set of values of x for which the binomial expansions of the f...

    Text Solution

    |

  9. Find the set of values of x for which the binomial expansions of the f...

    Text Solution

    |

  10. Write down the first three terms in the expansion of (3 + x)^(-3//2)

    Text Solution

    |

  11. Write down the first three terms in the expansion of (4 - 5x)^(-1//2)

    Text Solution

    |

  12. Write down and simplify 5th term in the expansion of (6 + 7x)^(-2)

    Text Solution

    |

  13. Write down and simplify 7th term in the expansion of (2 + 3x)^(-5)

    Text Solution

    |

  14. Prove that : Find the 10^("th")" term of "(1-(3x)/(4))^(4//5)

    Text Solution

    |

  15. Prove that : Find the 8^("th")" term of "(1-(5x)/(2))^(-3//5)

    Text Solution

    |

  16. 6th term of (3 + (2x)/(3))^(3//2)

    Text Solution

    |

  17. Prove that : Write the general term in the expansion of (1-4x)^(-3)

    Text Solution

    |

  18. Write the general term in the expansion of (3 - (5x)/(4))^(-1//2)

    Text Solution

    |

  19. Find the coefficient of x^5 in (3 - 4x)^(-1)

    Text Solution

    |

  20. Find the coefficient of x^4 in (8 - x)^(-1//3)

    Text Solution

    |