Home
Class 11
MATHS
If (1+x+x^(2) + "……" + x^(n))^(n) = a(0)...

If `(1+x+x^(2) + "……" + x^(n))^(n) = a_(0) + a_(1)x+a_(2)x^(2) + "….." a_(np) x^(np)`, then find the value of `a_(1) + 2a_(2) + 3a_(3) + "……" + np a_(np)`.

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

If (1+x-2x^(2))^(6) = 1 + a_(1)x+a_(2)x^(2) + "……" + a_(12)x^(12) , then find the value of a_(2) + a_(4) +a_(6)+ "……" + a_(12) .

If (1+x+2x^(2))^(20) = a_(0) + a_(1)x^() "……" + a_(40)x^(40) , then following questions. The value of a_(0) +a_(2) + a_(4)+ "……" + a_(38) is

If a_(1) = 2 and a_(n) - a_(n-1) = 2n (n ge 2) , find the value of a_(1) + a_(2) + a_(3)+…+a_(20) .

Let (1+x+x^(2))^(9)=a_(0)+a_(1)x+a_(2)x^(2)+.....+a_(18)x^(18) . Then

Let (1+x+x^(2))^(9)=a_(0)+a_(1)x+a_(2)x^(2)+......+a_(18)x^(18) . Then

If (1+x) ^(15) =a_(0) +a_(1) x +a_(2) x ^(2) +…+ a_(15) x ^(15), then the value of sum_(r=1) ^(15) r . (a_(r))/(a _(r-1)) is-

If (4x^(2) + 1)^(n) = sum_(r=0)^(n)a_(r)(1+x^(2))^(n-r)x^(2r) , then the value of sum_(r=0)^(n)a_(r) is

If (1+x-2x^2)^(20)=a_0+a_1x+a_2x^2+a_3x^3+...+a_(40)x^(40), then find the value of a_1+a_3+a_5+...+a_(39)dot

If (x^(2)+x+1)/(1-x) = a_(0) + a_(1)x+a_(2)x^(2)+"…." , then sum_(r=1)^(50) a_(r) equal to

If (1-x-x^(2))^(20) = sum_(r=0)^(40)a_(r).x^(r ) , then value of a_(1) + 3a_(3) + 5a_(5) + "….." + 39a_(39) is

CENGAGE PUBLICATION-BINOMIAL THEOREM-All Questions
  1. Find the value of 5C3 + 4C2

    Text Solution

    |

  2. Find the sum .^1C0+^2C1+^3C2+....+^(n+1)Cn ,where Cr=^n Crdot

    Text Solution

    |

  3. If (1+x+x^(2) + "……" + x^(n))^(n) = a(0) + a(1)x+a(2)x^(2) + "….." a(n...

    Text Solution

    |

  4. If n gt 2, then prove that C(1)(a-1) - C(2) xx (a-2) + "….." + (-1)^(...

    Text Solution

    |

  5. Find the sum C0-C2+C4-C6+ ......... ,where Cr=^n Cr .

    Text Solution

    |

  6. If x+y=1, prove that sum(r=0)^n .^nCr x^r y^(n-r) = 1.

    Text Solution

    |

  7. Find the sum 3 C1 + 5C2

    Text Solution

    |

  8. Prove that (.^(n)C(1))/(2) + (.^(n)C(3))/(4) + (.^(n)C(5))/(6) + "…." ...

    Text Solution

    |

  9. If (1+x)^n=sum(r=0)^n^n Cr , show that C0+(C1)/2++(Cn)/(n+1)=(2^(n+1...

    Text Solution

    |

  10. If underset(r=0)overset(2n)suma(r) (x-2)^(r) = underset(r=0)overset(2n...

    Text Solution

    |

  11. 3^(2n+2)-8n-9 is divisible by

    Text Solution

    |

  12. Statement 1: The number of distinct terms in (1+x+x^2+x^3+x^4)^(1000) ...

    Text Solution

    |

  13. The product of 3rd and 8th term of a GP is 243. If its 4th term is 3. ...

    Text Solution

    |

  14. The value of "^30C0.^30C10+^30C1.^30C11+^30C2.^30C(12)+……+^30C(20) . ^...

    Text Solution

    |

  15. If f(x)=x^n ,f(1)+(f^1(1))/1+(f^2(1))/(2!)+........(f^n(1))/(n !),w h ...

    Text Solution

    |

  16. The fractional part of =(2^(4n))/15 is

    Text Solution

    |

  17. The value of .^(15)C(0)^(2)-.^(15)C(1)^(2)+.^(15)C(2)^(2)-"...."-.^(15...

    Text Solution

    |

  18. If the sum of the coefficients in the expansion of (1-3x+10 x^2)^ni sa...

    Text Solution

    |

  19. If (1+x-2x^2)^6=1+a1x+a2x^2+……+a(12)x^12 then

    Text Solution

    |

  20. Maximum sum of coefficient in the expansion of (1-xsintheta+x^2)^n is

    Text Solution

    |