Home
Class 11
MATHS
Given, sn=1+q+q^2+.....+q^n ,Sn=1+(q+1)/...

Given, `s_n=1+q+q^2+.....+q^n ,S_n=1+(q+1)/2+((q+1)/2)^2+...` `+((q+1)/2)^n ,q!=1` prove that `"^(n+1)C_1+^(n+1)C_2s_1+^(n+1)C_3s_2+......+^(n+1)C_(n+1)s_n=2^n S_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 .^n C_0-^(n+1)C_1 . ^n C_1+^(n+2)C_2 . ^n C_2-=(-1)^ndot

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

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 , .^(2n)C_(n)=2^(n)(1.3.5...(2n-1))/(lfloorn)

Let S_n=1+q+q^2 +...+q^n and T_n =1+((q+1)/2)+((q+1)/2)^2+...((q+1)/2)^n If alpha T_100=^101C_1 +^101C_2 x S_1 ...+^101C_101 x S_100, then the value of alpha is

Show that : (^(4n)C_(2n))/(^(2n)C_n) = (1.3.5...(4n-1))/{1.3.5...(2n-1)}^2

Prove that .^(n)C_(0) +5 xx .^(n)C_(1) + 9 xx .^(n)C_(2) + "…." + (4n+1) xx .^(n)C_(n) = (2n+1) 2^(n) .

Prove that sum_(r=0)^ssum_(s=1)^n^n C_s^s C_r=3^n-1.

Prove that (.^(n)C_(1))/(2) + (.^(n)C_(3))/(4) + (.^(n)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) , prove that C_(0) *""^(2n)C_(n) - C_(1) *""^(2n-2)C_(n) + C_(2) *""^(2n-4) C_(n) -…= 2^(n)

CENGAGE PUBLICATION-BINOMIAL THEOREM-All Questions
  1. If n is a positive integer, prove that 1-2n+(2n(2n-1))/(2!)-(2n(2n-1)(...

    Text Solution

    |

  2. Find the third term from the end term of the GP.2/27, 2/9, 2/8,.........

    Text Solution

    |

  3. Given, sn=1+q+q^2+.....+q^n ,Sn=1+(q+1)/2+((q+1)/2)^2+... +((q+1)/2)^n...

    Text Solution

    |

  4. The sum of 1+n(1-1/x)+(n(n+1))/(2!)(1-1/x)^2+.....oo

    Text Solution

    |

  5. sum(k=1)^ook(1-1/n)^(k-1) =?

    Text Solution

    |

  6. The coefficient of x in the expansion of {sqrt(1+x^2)-x}^(-1) in ascen...

    Text Solution

    |

  7. 1+1/3x+(1xx4)/(3xx6)x^2+(1xx4xx7)/(3xx6xx9)x^3+------ is equal to

    Text Solution

    |

  8. The value of sum(r=1)^(15)(r2^r)/((r+2)!) is (a).((17)!-2^16)/((17)!) ...

    Text Solution

    |

  9. (n+2).^(n)C(0)2^(n+1).^(n)C(1)2^(n)+n.^(n)C(2)2^(n -1)-"…." is equal t...

    Text Solution

    |

  10. The value of underset(r=0)overset(20)sum(-1)^(r )(.^(50)C(r))/(r+2) is...

    Text Solution

    |

  11. In the expansion of [(1+x)(1-x)]^(2), the coefficient of x^(n) will be

    Text Solution

    |

  12. If a, b, c are in GP and a, x, b,y, c ar in AP. then prove that, 1...

    Text Solution

    |

  13. Statement 1: ""^m Cr+ ""^m C(r-1)(""^nC1)+ ""^mC(r-2)(""^n C2)+....+ "...

    Text Solution

    |

  14. 1+(1/4)+((1*3)/(4*8))+((1*4*7)/(4*8*12))+....=

    Text Solution

    |

  15. If |x|<1,then 1+n((2x)/(1+x))+(n(n+1))/(2!)((2x)/(1+x))^2+...... is eq...

    Text Solution

    |

  16. If a, b, c are in AP also in GP Then show that, a=b=c

    Text Solution

    |

  17. The sum of the GP (x+y)/(x-y), 1, (x-y)/(x+y),.....

    Text Solution

    |

  18. Statement 1: In the expansion of (1+x)^(41)(1-x+x^2)^(40), the coeffic...

    Text Solution

    |

  19. The coefficient of x^(n) in (1+x+(x^(2))/(2!) + (x^(3))/(3!) +"….." + ...

    Text Solution

    |

  20. Evaluate the following .^3C2

    Text Solution

    |