Home
Class 12
MATHS
Prove that (""^(2n)C(0))^(2)-(""^(2n)C...

Prove that
`(""^(2n)C_(0))^(2)-(""^(2n)C_(1))^(2)+(""^(2n)C_(2))-(""^(2n)C_(3))^(2)+......+(""^(2n)C_(2n))^(2)=(-1)^(n)""^(2n)C_(n).`

Promotional Banner

Topper's Solved these Questions

  • BINOMIAL THEOREM

    AAKASH SERIES|Exercise EXERCISE - 1.3 (Level - 1) |42 Videos

  • BINOMIAL THEOREM

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

  • BINOMIAL THEOREM

    AAKASH SERIES|Exercise EXERCISE - 1.1 (Level - 1) |52 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

""^(2n)C_(2)-2""^(n)C_(2)=

""^(2n)C_(n+1)+2. ""^(2n)C_(n) + ""^(2n) C_(n-1) =

Prove that (C_(0) +C_(1)+C_(2)+….+C_(n))^(2)=1 +""^(2n)C_(1) +""^(2n)C_(2) +…..+""^(2n)C_(2n)

""^(2n +1)C_0^2 -""^(2n+1)C_1^2 + ""^(2n+1)C_2^2 -…….- ""^(2n+1)C_(2n+1)^2 =

If ""^(n)C_(8)=""^(n)C_(2) , find ""^(n)C_(2) .

Show that (n !)/(x(x+1)(x+2)...(x+n))=(""^(n)C_(0))/(x)-(""^(n)C_(1))/(x+1) + (""^(n)C_(2))/(x+2)-(""^(n)C_(3))/(x+3) + ...+ ((-1)^(n)""^(n)C_(n))/(x+n) .

Prove that, C_(0) *""^(2n)C_(n)-C_(1)*""^((2n-2))C_(n)+C_(2) *""^((2n-4))C_(n)-…..=2^(n)

AAKASH SERIES-BINOMIAL THEOREM-EXERCISE - 1.2 (Level - 1)
  1. Prove the following: C(0)+2*C(1)+3*C(2)+…(n+1)*C(n)=(n+2).2^(n-1)

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

  4. Prove the following: 3*C(1)+7*C(2)+11*C(3)+…( 4n-1)*C(n)=1+(2n-1)...

    Text Solution

    |

  5. Prove the following: sum(r =0)^(n)(-1)^(r ) (3r+5).C(r )=0

    Text Solution

    |

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

    Text Solution

    |

  7. Prove the following: 1.2.C(1)+2.3C(2)+3.4.C(3)+….n(n+1).C(n) = n.(n+...

    Text Solution

    |

  8. Prove that : Prove that (C(1))/(C(0))+2.(C(2))/(C(1))+3.(C(3))/(C(2)...

    Text Solution

    |

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

    Text Solution

    |

  10. Prove that following (C(1))/(2)+(C(3))/(4)+(C(5))/(6)+(C(7))/(8)+……=...

    Text Solution

    |

  11. Prove the following: C(0)-(C(1))/(2)+(C(2))/(3) - …+(-1)^(n)(C(n))/...

    Text Solution

    |

  12. Prove that (""^(2n)C(0))^(2)-(""^(2n)C(1))^(2)+(""^(2n)C(2))-(""^(2n...

    Text Solution

    |

  13. Prove that (C(0)+C(1))(C(1)+C(2))(C(2)+C(3))....(C(n-1)+C(n))=((n+1)...

    Text Solution

    |

  14. Prove that (C(0) +C(1)+C(2)+….+C(n))^(2)=1 +""^(2n)C(1) +""^(2n)C(2)...

    Text Solution

    |

  15. Use the identity (1+x)^(m)(1+x)^(n)=(1+x)^(m+n) to prove Vandermonde's...

    Text Solution

    |

  16. Find the sum of the series C(1)+2^(2) *C(2)x+3^(2)*C(3)x^(2)+4^(2)*C(4...

    Text Solution

    |

  17. Show that (2^(2) *C(0) )/(1*2)+(2^(3)*C(1))/(2*3)+(2^(4) *C(2))/(3*4)+...

    Text Solution

    |

  18. Show that ""^(n)C(0) +""^((n+1))C(1) +""^((n+2))C(2) +…+""^((n+k))C(k)...

    Text Solution

    |

  19. Show that ""^(30)C(0) +""^(30)C(1)+""^(30)C(2) +…+ ""^(30)C(14) =2^(29...

    Text Solution

    |