Home
Class 11
MATHS
Let a=(2^(1//401)-1) and for each ngeq2...

Let `a=(2^(1//401)-1)` and for each `ngeq2,l e tb_n=^n C_1+^n C_2dota+^n C_3a^2+......+^n C_n*a^(n-1)` . Find the value of `(b_(2006)-b_(2005))dot`

Text Solution

AI Generated Solution

Promotional Banner

Topper's Solved these Questions

  • COMPLEX NUMBERS AND QUADRATIC EQUATIONS

    CENGAGE ENGLISH|Exercise All Questions|886 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

Find the sum 3^n C_0-8^n C_1+13^n C_2xx^n C_3+dot

Prove that ^n C_1(^n C_2)(^n C_3)^3(^n C_n)^nlt=((2^n)/(n+1))^(n+1_C()_2),AAn in Ndot

Prove that .^n C_0 . ^(2n) C_n- ^n C_1 . ^(2n-2)C_n+^n C_2 . ^(2n-4)C_n-=2^ndot

Prove that nC_1(nC_2)^2(n C_3)^3.......(n C_n)^n le ((2^n)/(n+1))^((n+1)C_2),AAn in Ndot

If (1+x)^n=sum_(r=0)^n C_r x^r , then prove that C_1+2C_2+3C_3+....+n C_n=n2^(n-1)dot .

The value of ^n C_1+^(n+1)C_2+^(n+2)C_3++^(n+m-1)C_m is equal to

Prove that "^n C_0^(2n)C_n-^n C_1^(2n-1)C_n+^n C_2xx^(2n-2)C_n++(-1)^n^n C_n^n C_n=1.

(n+2)C_0(2^(n+1))-(n+1)C_1(2^(n))+(n)C_2(2^(n-1))-.... is equal to

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 .

CENGAGE ENGLISH-BINOMIAL THEOREM-All Questions
  1. For any positive integer (m,n) (with ngeqm), Let ((n),(m)) =.^nCm Prov...

    Text Solution

    |

  2. If sum(r=0)^n{ar(x-alpha+2)^r-br(alpha-x-1)^r}=0, then prove that bn-(...

    Text Solution

    |

  3. Let a=(2^(1//401)-1) and for each ngeq2,l e tbn=^n C1+^n C2dota+^n C3...

    Text Solution

    |

  4. Prove that sum(r=0)^n^n Cr(-1)^r[i^r+i^(2r)+i^(3r)+i^(4r)]=2^n+2^(n/2+...

    Text Solution

    |

  5. Find the coefficient of x^n in (1+x/(1!)+(x^2)/(2!)+........+(x^n)/(n ...

    Text Solution

    |

  6. Prove that (^n C0)/x-(^n C0)/(x+1)+(^n C1)/(x+2)-+(-1)^n(^n Cn)/(x+n)=...

    Text Solution

    |

  7. If n is a positive integer, prove that 1-2n+(2n(2n-1))/(2!)-(2n(2n-1)(...

    Text Solution

    |

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

    Text Solution

    |

  9. The sum of 1+n(1-1/x)+(n(n+1))/(2!)(1-1/x)^2+oo will be a. x^n b. x^(-...

    Text Solution

    |

  10. sum(k=1)^ook(1-1/n)^(k-1)=>? a.n(n-1) b. n(n+1) c. n^2 d. (n+1)^2

    Text Solution

    |

  11. The coefficient of x^4 in the expansion of {sqrt(1+x^2)-x}^(-1) in asc...

    Text Solution

    |

  12. 1+1/3x+(1xx4)/(3xx6)x^2+(1xx4xx7)/(3xx6xx9)x^3+------ is equal to a. x...

    Text Solution

    |

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

    Text Solution

    |

  14. (n+2)C0(2^(n+1))-(n+1)C1(2^(n))+(n)C2(2^(n-1))-.... is equal to

    Text Solution

    |

  15. The value of sum(r=0)^(50)(-1)^r((50)Cr)/(r+2) is equal to a . 1/(50x...

    Text Solution

    |

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

    Text Solution

    |

  17. Statement : The sum of coefficient in the expansion of (3^(-x//4)+3^(5...

    Text Solution

    |

  18. Let n be a positive integer and k be a whole number, klt=2ndot Statem...

    Text Solution

    |

  19. Statement 1: sum sum(0le ilt j le n)(i/ (.^n ci)+j/(.^ncj)) is equal t...

    Text Solution

    |

  20. Statement 1: ^m Cr+^m C(r-1)(^nC1)+^mC(r-2)(^n C2)+....+^n Cr=0 , if m...

    Text Solution

    |