Home
Class 12
MATHS
(1-x)^(n)=C(0)-C(1)x+C(2)x^(2)-C(3)x^(3)...

`(1-x)^(n)=C_(0)-C_(1)x+C_(2)x^(2)-C_(3)x^(3)+...+C_(r)(-1)^(r)x^(r)+.....+(-1)^(n)x^(n)`
Show that , `C_(1)+2C_(2)+3C_(3)+.....+n.C_(n)=n.2^(n-1)`

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_(1)+2.C_(2)+3.C_(3)+....+n.C_(n)=n.2^(n-1)

If (1+x)^(n)=C_(0)+C_(1)x+C_(2)x^(2)+.....+C_(n)x^(n) then show : C_(0)+4C_(1)+8C_(2)+12C_(3)+......+4nC_(n)=1+n.2^(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) Show that C_(1)^(2)+2*C_(2)^(2)+3*C_(3)^(2)....+n*C_(n)^(2)=((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))/(C_(0))+(2C_(2))/(C_(1))+(3C_(3))/(C_(2))+....+(nC_(n))/(C_(n-1))=(n(n-1))/(2)

If (1+x)^(n)=^(n)C_(0)+^(n)C_(1)x+^(n)C_(2)x^(2)+…+^(n)C_(n)x^(n) , prove that, nC_(1)-2^(n)C_(2)+3^(n)C_(3)-…+(-1)^(n-1).n^(n)C_(n)=0 .

If (1+x)^(n)=C_(0)+C_(1)+x+C_(2)x^(2)+...+C_(n)x^(n) show that, C_(0)-2^(2)*C_(1)+3^(2)*C_(2)-...+(-1)^(n)*(n+1)^(2)*C_(n)=0 (n gt 2)

If (1+x)^(n)=^(n)C_(0)+^(n)C_(1)x+^(n)C_(2)x^(2)+…+^(n)C_(n)x^(n) , prove that, nC_(0) +2^(n)C_(1)+3^(n)C_(2)+…+(n+1)^(n)C_(n)=(n+2)*2^(n-1) .

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)!)

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 :

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

  6. (1-x)^(n)=C(0)-C(1)x+C(2)x^(2)-C(3)x^(3)+...+C(r)(-1)^(r)x^(r)+.....+(...

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

  14. Find numerically the greatest terms in the following expansion : [1...

    Text Solution

    |

  15. Find numerically the greatest terms in the following expansion : {(2x...

    Text Solution

    |

  16. Find numerically the greatest terms in the following expansion (ax-...

    Text Solution

    |

  17. Find numerically the greatest cofficients in the following expansions ...

    Text Solution

    |

  18. Find numerically the greatest cofficients in the following expansions ...

    Text Solution

    |

  19. Which terms in the expansion of (x+(1)/(2x))^(3n) has the greatest coe...

    Text Solution

    |

  20. In the expansion of the expression (a+x)^(15) ,if the eleventh term i...

    Text Solution

    |