Home
Class 12
MATHS
If a(r) is the coefficient of x^(r ) in ...

If `a_(r)` is the coefficient of `x^(r )` in the expansion of `(1+x+x^(2))^(n)(n in N)`. Then the value of `(a_(1)+4a_(4)+7a_(7)+10a_(10)+……..)` is equal to :

A

`3^(n-1)`

B

`2^(n)`

C

`(1)/(3)*2^(n)`

D

`n*3^(n-1)`

Text Solution

Verified by Experts

The correct Answer is:
D
Promotional Banner

Topper's Solved these Questions

  • BIONMIAL THEOREM

    VK JAISWAL|Exercise Exercise-2 : One or More than One Answer is/are Correct|9 Videos

  • BIONMIAL THEOREM

    VK JAISWAL|Exercise Exercise-3 : Matching Type Problems|3 Videos

  • AREA UNDER CURVES

    VK JAISWAL|Exercise EXERCISE (SUBJECTIVE TYPE PROBLEMS)|8 Videos

  • CIRCLE

    VK JAISWAL|Exercise Exercise - 5 : Subjective Type Problems|13 Videos

Similar Questions

Explore conceptually related problems

If a_(r) is the coefficient of x^(r) in the expansion of (1+x+x^(2))^(n), then a_(1)-2a_(2)+3a_(3)....-2na_(2n)=

If a_(r) be the coefficient of x^(r) in the expression of (1+bx^(2)+cx^(3))^(n), then prove that,2na_(4)=(n-1)a_(2)^(2)

If a_(k) is the coefficient of x^(k) in the expansion of (1+x+x^(2))^(n) for k=0,1,2,......,2n then a_(1)+2a_(2)+3a_(3)+...+2na_(2n)=

If a_(r) is the coefficient of x^(r) in (1-2x+3x^(2))^(n), then sum_(r=0)^(2n)r*a_(r)=

in If the coefficient of x^(r) and x^(r+1) are equal in the expansion of (1+x)^(2n+1), then find the value of r.

For r=0,1,.....,10, let A_(r),B_(r),quad and C_(r) denote,respectively,the coefficient of x^(r) in the expansions of (1+x)^(10),(+x)^(20) and (1+x)^(30). Then sum A_(r)(B_(10)B_(r)-C_(10)A_(r)) is equal to

If a_(0), a_(1), a(2),… are the coefficients in the expansion of (1 + x + x^(2))^(n) in ascending powers of x, prove that a_(0) a_(2) - a_(1) a_(3) + a_(2) a_(4) - …+ a_(2n-2) a_(2n)= a_(n+1) .

VK JAISWAL-BIONMIAL THEOREM-Exercise-4 : Subjective Type Problems
  1. If a(r) is the coefficient of x^(r ) in the expansion of (1+x+x^(2))^(...

    Text Solution

    |

  2. The sum of series 3*""^(2007)C(0)-8*""^(2007)C(1)+13*""^(2007)C(2)-18...

    Text Solution

    |

  3. In the polynomial function f(x)=(x-1)(x^(2)-2)(x^(3)-3)……..(x^(11)-11...

    Text Solution

    |

  4. If sum(r=0)^(3n)a(r)(x-4)^(r )=sum(r=0)^(3n)A(r)(x-5)^(r ) and a( k)=1...

    Text Solution

    |

  5. If 3^(101)-2^(100) is divided by 11, the remainder is

    Text Solution

    |

  6. Find the hundred's digit in the co-efficient of x^(17) in the expansio...

    Text Solution

    |

  7. Let n in N, Sn=sum(r=0)^(3n)^(3n)Cr and Tn=sum(r=0)^n^(3n)C(3r), then ...

    Text Solution

    |

  8. Find the sum of possible real values of x for which the sixth term of ...

    Text Solution

    |

  9. Let q be a positive with q le 50. If the sum ""^(98)C(30)+2" "^(97)C...

    Text Solution

    |

  10. The remainder when (sum(k=1)^(5) ""^(20)C(2k-1))^(6) is divided by 11,...

    Text Solution

    |

  11. Let a=3^(1/(223))+1 and for all geq3,l e tf(n)=^n C0dota^(n-1)-^n C1do...

    Text Solution

    |

  12. In the polynomial function f(x)=(x-1)(x^(2)-2)(x^(3)-3)……..(x^(11)-11...

    Text Solution

    |

  13. Let the sum of all divisiors of the form 2^(p)*3^(q) (with p, q posit...

    Text Solution

    |

  14. For what value of x is the ninth term in the expansion of (3^(log3 sqr...

    Text Solution

    |

  15. Let 1+ sum(r=1)^10 (3^r C(10,r) + r C(10,r))=2^10 (alpha 4^5+beta) whe...

    Text Solution

    |

  16. Let S(n)=""^(n)C(0)""^(n)C(1)+""^(n)C(1)""^(n)C(2)+…..+""^(n)C(n-1)""^...

    Text Solution

    |