Home
Class 12
MATHS
If (1+x)^(n)=C(0)+C(1)x+C(2)x^(2)+.....+...

If `(1+x)^(n)=C_(0)+C_(1)x+C_(2)x^(2)+.....+C_(n)x^(n)` then show :
`(C_(1))/(C_(0))+(2C_(2))/(C_(1))+(3C_(3))/(C_(2))+....+(nC_(n))/(C_(n-1))=(n(n-1))/(2)`

Promotional Banner

Topper's Solved these Questions

  • BINOMIAL THEOREM

    CHHAYA PUBLICATION|Exercise Sample Questions for Competitive Exams (Multiple Correct Answers Type)|5 Videos

  • BINOMIAL THEOREM

    CHHAYA PUBLICATION|Exercise Sample Questions for Competitive Exams (Integer Answer Type)|5 Videos

  • BINOMIAL THEOREM

    CHHAYA PUBLICATION|Exercise EXERCISE ( short answer Type Questions )|53 Videos

  • BINOMIAL DISTRUTION

    CHHAYA PUBLICATION|Exercise ASSERTION-REASON TYPE|2 Videos

  • CALCULUS

    CHHAYA PUBLICATION|Exercise JEE Advanced Archive (2014)|2 Videos

Similar Questions

Explore conceptually related problems

If (1+x)^(n)=C_(0)+C_(1)x+C_(2)x^(2)+.....+C_(n)x^(n) then show : (C_(0))/(1)+(C_(2))/(3)+(C_(4))/(5)+....=(2^(n))/(n+1)

If (1+x)^(n)=C_(0)+C_(1)x+C_(2)x^(2)+.....+C_(n)x^(n) then show : (C_(1))/(2)+(C_(3))/(4)+(C_(5))/(6)+....=(2^(n)-1)/(n+1)

If (1+x)^(n)=C_(0)+C_(1)x+C_(2)x^(2)+.....+C_(n)x^(n) then show : C_(1)-2C_(2)+3C_(3)-....+(-1)^(n-1)n.C_(n)=0

If (1+x)^(n)=C_(0)+C_(1)x+C_(2)x^(2)+.....+C_(n)x^(n) then show : (C_(0))/(1)+(C_(1))/(2)+(C_(2))/(3)+......+(C_(n))/(n+1)=(2^(n+1)-1)/(n+1)

If (1+x)^(n)=C_(0)+C_(1)x+C_(2)x^(2)+.....+C_(n)x^(n) then show : (C_(0))/(1)-(C_(1))/(2)+(C_(2))/(3)-......+(-1)^(n).(C_(n))/(n+1)=(1)/(n+1)

If (1+x)^(n)=C_(0)+C_(1)x+C_(2)x^(2)+.....+C_(n)x^(n) then show : C_(0).C_(n)+C_(1).C_(n-1)+C_(2).C_(n-2)+....+C_(n).C_(0)=((2n)!)/((n!)^(2))

The value of (1+(C_(1))/(C_(0))) (1+ (C_(2))/(C_(1)))(1+ (C_(3))/(C_(2)))...(1+ (C_(n))/(C_(n-1))) is-

If (1+x)^(n)=C_(0)+C_(1)x+C_(2)x^(2)+.....+C_(n)x^(n) then show : C_(0)C_(1)+C_(1)C_(2)+C_(2)C_(3)+.....+C__(n-1)C_(n)=((2n)!)/((n+1)!(n-1)!)

If (1+x)^(n)=C_(0)+C_(1)x+C_(2)x^(2)+.....+C_(n)x^(n) then show : C_(0)^(2)+(C_(1)^(2))/(2)+(C_(2)^(2))/(3)+.....+(C_(n)^(2))/(n+1)=((2n+1)!)/({(n+1)!}^(2))

If (1+x)^(n)=C_(0)+C_(1)x+C_(2)x^(2)+.....+C_(n)x^(n) then show : C_(1)+2.C_(2)+3.C_(3)+....+n.C_(n)=n.2^(n-1)

CHHAYA PUBLICATION-BINOMIAL THEOREM -EXERCISE ( Long answer Type Questions )
  1. If (1+x)^(n)=C(0)+C(1)x+C(2)x^(2)+.....+C(n)x^(n) then show : C(0)...

    Text Solution

    |

  2. If (1+x)^(n)=C(0)+C(1)x+C(2)x^(2)+.....+C(n)x^(n) then show : C(0)...

    Text Solution

    |

  3. If (1+x)^(n)=C(0)+C(1)x+C(2)x^(2)+.....+C(n)x^(n) then show : (C(1...

    Text Solution

    |

  4. If (1+x)^(n)=C(0)+C(1)x+C(2)x^(2)+.....+C(n)x^(n) then show : (C(0...

    Text Solution

    |

  5. If (1+x)^(n)=C(0)+C(1)x+C(2)x^(2)+.....+C(n)x^(n) then show : (C(1)...

    Text Solution

    |

  6. If (1+x)^(n)=C(0)+C(1)x+C(2)x^(2)+.....+C(n)x^(n) then show : C(0)...

    Text Solution

    |

  7. If (1+x)^(n)=C(0)+C(1)x+C(2)x^(2)+.....+C(n)x^(n) then show : C(0)...

    Text Solution

    |

  8. If (1+x)^(n)=C(0)+C(1)x+C(2)x^(2)+.....+C(n)x^(n) then show :

    Text Solution

    |

  9. If (1+x)^(n)=C(0)+C(1)x+C(2)x^(2)+.....+C(n)x^(n) then show :

    Text Solution

    |

  10. If (1+x)^(n)=C(0)+C(1)x+C(2)x^(2)+.....+C(n)x^(n) then show :

    Text Solution

    |

  11. If (1+x)^(n)=C(0)+C(1)x+C(2)x^(2)+.....+C(n)x^(n) then show : 3.^(...

    Text Solution

    |

  12. The power of a of 10thterm in the extension (a+2b)^20-

    Text Solution

    |

  13. (1-x)^(n)=C(0)-C(1)x+C(2)x^(2)-C(3)x^(3)+...+C(r)(-1)^(r)x^(r)+.....+(...

    Text Solution

    |

  14. Find the sum of the series .^(n)C(0)+2.^(n)C(1)x+3.^(n)C(2)x^(2)+......

    Text Solution

    |

  15. Show : x-^(n)C(1)(x+y)+^(n)C(2)(x+2y)-^(n)C(3)(x+3y)+....=0

    Text Solution

    |

  16. Show : 2^(n)-(n)/(1!).2^(n-1)+(n(n-1))/(2!).2^(n-2)-....+(-1)^(n)=1

    Text Solution

    |

  17. If (1+x)^(n)=C(0)+C(1)x+C(2)x^(2)+...+C(n)x^(n) "show that ", (1)/(1...

    Text Solution

    |

  18. Find numerically the greatest terms in the following expansion : (1...

    Text Solution

    |

  19. Find numerically the greatest terms in the following expansion : (1-...

    Text Solution

    |

  20. Find numerically the greatest terms in the following expansion : (2...

    Text Solution

    |