Home
Class 11
MATHS
If n=12 m(m in N), prove that .^n C0-(...

If `n=12 m(m in N),` prove that
`.^n C_0-(.^n C_2)/((2+sqrt(3))^2)+(.^n C_4)/((2+sqrt(3))^4)-(.^n C_6)/((2+sqrt(3))^6)+.......=` ` (-1)^m((2sqrt(2))/(1+sqrt(3)))^ndot`

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)/1+(.^n C_2)/3+(.^n C_4)/5+(.^n C_6)/7+ . . . =(2^n)/(n+1)dot

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) .

Prove that .^n C_0+^n C_3+^n C_6+=1/3(2^n+2cos((npi)/3)) .

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

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

Prove that (.^(n)C_(1))/(2) + (.^(n)C_(3))/(4) + (.^(n)C_(5))/(6) + "…." = (2^(n) - 1)/(n+1) .

lim_(n to oo)[(1)/(sqrt(n^(2)-1^(2)))+(1)/(sqrt(n^(2)-2^(2)))+(1)/(sqrt(n^(2)-3^(2)))+...+(1)/(sqrt(n^(2)-(n-1)^(2)))]

lim_(nto oo)[(sqrt(n+1)+sqrt(n+2)+...+sqrt(2)n)/(sqrt(n^(3)))]

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

If tanA+sinA=m and tanA-sinA=n , then prove that m^(2)-n^(2)=4sqrt(mn) .

CENGAGE PUBLICATION-BINOMIAL THEOREM-All Questions
  1. If a, b, c are in AP, a, x, b are in GP , where as b, y and c also in...

    Text Solution

    |

  2. Prove that 1/(m !).^n C0+n/((m+1)!).^n C1+(n(n-1))/((m+2)!).^n C2+.......

    Text Solution

    |

  3. If n=12 m(m in N), prove that .^n C0-(.^n C2)/((2+sqrt(3))^2)+(.^n C...

    Text Solution

    |

  4. Prove that in the expansion of (1+x)^(n) (1+y)^(n) (1+z)^(n), the sum ...

    Text Solution

    |

  5. Prove that .^100 C0^(100)C2+^(100)C2^(100)C4+^(100)C4^(100)C6++^(100)C...

    Text Solution

    |

  6. Prove that sum(r=1)^(m-1)(2r^2-r(m-2)+1)/((m-r)^m Cr)=m-1/mdot

    Text Solution

    |

  7. Find the coefficients of x^(50) in the expression (1+x)^(1000)+x(1+x)^...

    Text Solution

    |

  8. If a, b, c are in GP and a, x, b, y are in AP Then prove that, a/x + ...

    Text Solution

    |

  9. If .^(n+1)C(r+1):^n Cr:^(n-1)C(r-1)=11 :6:3, then n r= 20 b. 30 c. 40...

    Text Solution

    |

  10. If the last tem in the binomial expansion of (2^(1/3)-1/(sqrt(2)))^n i...

    Text Solution

    |

  11. Find the last two digits of the number (23)^(14)dot

    Text Solution

    |

  12. The value of x for which the sixth term in the expansion of [2^(log(...

    Text Solution

    |

  13. If the 6th term in the expansion of (1/x^(8//3)+x^2log(10)x)^8 is 5600...

    Text Solution

    |

  14. The total number of terms which are dependent on the value of x in the...

    Text Solution

    |

  15. In the expansion of (3^(-x//4)+3^(5x//4))^(n) the sum of binomial coef...

    Text Solution

    |

  16. If n is an integer between 0 and 21, then the minimum value of n!(21-n...

    Text Solution

    |

  17. If R is remainder when 6^(83)+8^(83) is divided by 49, then find the v...

    Text Solution

    |

  18. Let a and b be the coefficient of x^(3) in (1+x+2x^(2) + 3x^(3))^(4) a...

    Text Solution

    |

  19. Let 1+ underset(r=1)overset(10)sum(3^(r)..^(10)C(r)+r..^(10)C(r)) = 2^...

    Text Solution

    |

  20. Let a=3^(1//224)+1 and for all n ge 3, let f(n)=""^(n)C(0)a^(n-1)-""...

    Text Solution

    |