Home
Class 12
MATHS
If n is a positive integer and C4 = ""^n...

If n is a positive integer and `C_4 = ""^nC_r` then find the value of `sum_(x = 1)^n r^2 ((C_r)/(C_(r - 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

If n is a positive integer and C_(r )= ""^(n)C_(r ) then find the vlaue of sum_(r =1)^(n) r^(2)((C_(r ))/(C_(r -1))) .

The value of sum_(r = 1)^15 r^2 ((""^15C_r)/(""^15C_(r - 1)) ) of is equal to

sum_(r = 0)^(n-1) (C_r)/(C_r + C_(r+1)) =

sum_(r=1)^(10) r. (""^nC_r)/(""^nC_(r-1)) =

Prove that sum_(r = 1)^n r^3 ((C_r)/(C_(r - 1))^2) = (n (n + 1)^2 (n+2))/(12)

If n is a positive integer, prove that sum_(r=1)^(n)r^(3)((""^(n)C_(r))/(""^(n)C_(r-1)))^(2)=((n)(n+1)^(2)(n+2))/(12)

sum_(r=1)^(n) (-1)^(r-1) ""^nC_r(a - r) =

Prove that sum_(r = 0)^n r^2 . C_r = n (n +1).2^(n-2)

Prove that sum_(k=1)^(n-r ) ""^(n-k)C_(r )= ""^(n)C_( r+1) .

AAKASH SERIES-BINOMIAL THEOREM-SOLVED EXAMPLES
  1. With usual notations prove that C1+2.C2x + 3.C3x^2 + ……+2n.C(2n) ...

    Text Solution

    |

  2. Prove that (""^20C1)/(""^20C0) + 2. (""^20C2)/(""^20C1) + 3. (""^2...

    Text Solution

    |

  3. If n is a positive integer and C4 = ""^nCr then find the value of sum(...

    Text Solution

    |

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

    Text Solution

    |

  5. Prove that sum(r = 0)^n r^2 . Cr = n (n +1).2^(n-2)

    Text Solution

    |

  6. Prove that sum(r = 0)^n r^3 . Cr = n^2 (n +3).2^(n-3)

    Text Solution

    |

  7. If Cr denotes ""^nCr then show that C0 + (C1)/(2) + (C2)/(3) x^2 +...

    Text Solution

    |

  8. If C0, C1, C2 ,……..Cn are the coefficient in the expansion of (1 + x)^...

    Text Solution

    |

  9. With usual notations prove that C0 + 3.C1 + 3^2.C2 + ………..+3^n .Cn...

    Text Solution

    |

  10. With usual notations prove that C1/C0 + 2. C2/C1 + 3.C3/C2 + ……+n.(...

    Text Solution

    |

  11. Prove that (C0 + C1) (C1 + C2) …..(C(n-1) + Cn) = ((n+1)^n)/(n!) (C1.C...

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |