Home
Class 11
MATHS
Prove that ^mC1^n Cm-^m C2^(2n)Cm+^m C3^...

Prove that `^mC_1^n C_m-^m C_2^(2n)C_m+^m C_3^(3n)C_m-.....=(-1)^(m-1)n^mdot`

Promotional Banner

Topper's Solved these Questions

  • COMPLEX NUMBERS AND QUADRATIC EQUATIONS

    CENGAGE PUBLICATION|Exercise All Questions|877 Videos

Similar Questions

Explore conceptually related problems

Prove that .^n C_0 .^n C_0-^(n+1)C_1 . ^n C_1+^(n+2)C_2 . ^n C_2- .. =(-1)^n .

Using binomial theorem (without using the formula for .^n C_r ) , prove that .^nC_4+^m C_2-^m C_1.^n C_2 = .^m C_4-^(m+n)C_1.^m C_3+^(m+n)C_2.^m C_2-^(m+n)C_3^m.C_1 +^(m+n)C_4dot

Prove that 1/(n+1)=(.^n C_1)/2-(2(.^n C_2))/3+(3(.^n C_3))/4- . . . +(-1^(n+1))(n*(.^n C_n))/(n+1) .

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 .

Prove that (C_0+C_1)(C_1+C_2)(C_2+C_3)(C_3+C_4)...........(C_(n-1)+C_n) = (C_0C_1C_2.....C_(n-1)(n+1)^n)/(n!)

Prove that .^(n)C_(1) + 2 xx .^(n)C_(2) + 3 xx .^(n)C_(3) + "…." + n xx .^(n)C_(n) = n2^(n-1) . Hence, prove that .^(n)C_(1).(.^(n)C_(2))^(2).(.^(n)C_(3))^(3)"......."(.^(n)C_(n))^(n) le ((2^(n))/(n+1))^(.^(n+1)C_(2)) AA n in N .

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

Prove that (C_1)/1-(C_2)/2+(C_3)/3-(C_4)/4+....+((-1)^(n-1))/n C_n=1+1/2+1/3+...+1/n

If m= ^nC_2 show that ^mC_2=3^(n+1)C_4

Prove that sum_(r=1)^(m-1)(2r^2-r(m-2)+1)/((m-r)^m C_r)=m-1/mdot

CENGAGE PUBLICATION-BINOMIAL THEOREM-All Questions
  1. If p+q=1, then show that sum(r=0)^nr^2^nCrp^rq^(n-r)=npq+n^2p^2

    Text Solution

    |

  2. If every pair from among the equations x^2+a x+b c=0. x^2+b x+c a=0,a ...

    Text Solution

    |

  3. Prove that ^mC1^n Cm-^m C2^(2n)Cm+^m C3^(3n)Cm-.....=(-1)^(m-1)n^mdot

    Text Solution

    |

  4. Prove that ^nC0 "^(2n)Cn-^nC1 ^(2n-2)Cn +^nC2 ^(2n-4)Cn =2^n

    Text Solution

    |

  5. Find the sum sum(r=0) .^(n+r)Cr .

    Text Solution

    |

  6. Find the value of (sumsum)(0leiltjlen) (i+j)(""^(n)C(i)+""^(n)C(j)).

    Text Solution

    |

  7. Find the sum sumsum(0lt=i<jlt=n-1)^n Cidot

    Text Solution

    |

  8. Find the value of underset(0leiltjlen)(sumsum)(.^(n)C(i)+.^(n)C(j)).

    Text Solution

    |

  9. Find the sum (sumsum)(0leiltjlen) ""^(n)C(i).""^(n)C(j).

    Text Solution

    |

  10. Prove that sum(r=0)^ssum(s=1)^n^n Cs^s Cr=3^n-1.

    Text Solution

    |

  11. Find the sum sumsum(0leiltjlen)"^nCi

    Text Solution

    |

  12. Find the coefficient of x^4 in the expansion of (x/2-3/x^2)^10.

    Text Solution

    |

  13. Find the term in(3sqrt(((a)/(sqrt(b))) + (sqrt((b)/ (3sqrt(a))))^(21) ...

    Text Solution

    |

  14. Using the binomial theorem, evaluate (102)^5 .

    Text Solution

    |

  15. Find the 6th term in expansion of (2x^2-1/(3x^2))^(10)dot

    Text Solution

    |

  16. Find a, if 17th and 18th terms in the expansions of (2+a)^50 are equal...

    Text Solution

    |

  17. Find n , if the ratio of the fifth term from the beginning to the ...

    Text Solution

    |

  18. Simplify: x^5+10 x^4a+40 x^3a^2+80 x^2a^3+80 x a^4+32 a^5dot

    Text Solution

    |

  19. Find the value of (18^3+7^3+3.18.7.25) /(3^6+6.243.2+15.81.4+20.27.8+1...

    Text Solution

    |

  20. Find the approximation of (0. 99)^5 using the first three terms of its...

    Text Solution

    |