Home
Class 11
MATHS
Sum the series : 1(2-omega)(2-omega^(2))...

Sum the series : `1(2-omega)(2-omega^(2))+2(3-omega)(3-omega^(2))......(n-1)(n-omega)(n-omega^(2))` where `omega` and `omega^(2)` are non-real cube roots of unity.

Promotional Banner

Topper's Solved these Questions

  • SEQUENCES AND SERIES

    MODERN PUBLICATION|Exercise EXERCISE|435 Videos

  • RELATIONS AND FUNCTIONS

    MODERN PUBLICATION|Exercise EXERCISE|226 Videos

  • SETS

    MODERN PUBLICATION|Exercise EXERCISE|381 Videos

Similar Questions

Explore conceptually related problems

Value of |{:(1,omega,omega^(2)),(omega,omega^(2),1),(omega^(2),1,omega):}| is zero, where omega,omega^(2) are imaginary cube roots of unity.

Show that a=r omega^(2) .

If omega(ne1) is a cube root of unity, then (1-omega+omega^(2))(1-omega^(2)+omega^(4))(1-omega^(4)+omega^(8)) …upto 2n is factors, is

If omega^(3)=1 and omega ne1 , then (1+omega)(1+omega^(2))(1+omega^(4))(1+omega^(5)) is equal to

Let omega ne 1 be a complex cube root of unity. If (3-3omega+2omega^(2))^(4n+3) + (2+3omega-3omega^(2))^(4n+3)+(-3+2omega+3omega^(2))^(4n+3)=0 , then the set of possible value(s) of n is are

If omega!=1 is a complex cube root of unity, then prove that [{:(1+2omega^(2017)+omega^(2018)," "omega^(2018),1),(1,1+2omega^(2018)+omega^(2017),omega^(2017)),(omega^(2017),omega^(2018),2+2omega^(2017)+omega^(2018)):}] is singular

If 1,alpha_1,alpha_2,alpha_3,alpha_4 be the roots x^5-1=0 , then value of [omega-alpha_1]/[omega^2-alpha_1].[omega-alpha_2]/[omega^2-alpha_2].[omega-alpha_3]/[omega^2-alpha_3].[omega-alpha_4]/[omega^2-alpha_4] is (where omega is imaginary cube root of unity)

If omega ne 1 and omega^3=1 , then : (a omega+b+c omega^2)/(a omega^2+b omega+c) + (a omega^2+b+c omega)/(a+b omega+c omega^2) is equal to :

If omega = (-1+sqrt3i)/2 , find the value of |(1, omega, omega^2),(omega, omega^2, 1),(omega^2, 1 , omega)|

If x, y, z are not all zero & if ax + by + cz=0, bx+ cy + az=0 & cx + ay + bz = 0 , then prove that x: y : z = 1 : 1 : 1 OR 1 :omega:omega^2 OR 1:omega^2:omega , where omega is one ofthe complex cube root of unity.

MODERN PUBLICATION-SEQUENCES AND SERIES-EXERCISE
  1. Sum the series : 1(2-omega)(2-omega^(2))+2(3-omega)(3-omega^(2)).........

    Text Solution

    |

  2. Write the first three terms of the sequence defined by the following :...

    Text Solution

    |

  3. Write the first five terms of the sequences given below whose nth term...

    Text Solution

    |

  4. Write the first five terms of the following functions whose nth terms ...

    Text Solution

    |

  5. Write the first four terms of the following sequence whose nth terms a...

    Text Solution

    |

  6. Write the first four terms of the following sequence whose nth terms a...

    Text Solution

    |

  7. Write the first four terms of the following sequence whose nth terms a...

    Text Solution

    |

  8. Write the first four terms of the following sequence whose nth terms a...

    Text Solution

    |

  9. Write the first four terms of the following sequence whose nth terms a...

    Text Solution

    |

  10. Write the first five terms of the following sequence whose nth terms a...

    Text Solution

    |

  11. Write the first five terms of the following sequence whose nth terms a...

    Text Solution

    |

  12. Write the first five terms of the following sequence whose nth terms a...

    Text Solution

    |

  13. Write the first five terms of the sequences given below whose nth term...

    Text Solution

    |

  14. Write the first five terms of the sequences given below whose nth term...

    Text Solution

    |

  15. What is the 19th term of the sequence : a(n) = (n(n-2))/(n+3)?

    Text Solution

    |

  16. Find the term indicated in the following case : t(n)=4^(n)+n^(2)-n+1...

    Text Solution

    |

  17. Find the term indicated in the following case : h(n)=n^(2)-3n+4, h(1...

    Text Solution

    |

  18. Find the term indicated in the following case : an= n^2/2^n , a7.

    Text Solution

    |

  19. Find the term indicated in the following case : an= (-1)^(n-1) n^3 ,...

    Text Solution

    |

  20. Find the term indicated in the following case : an= (n(n-2))/(n-3), ...

    Text Solution

    |

  21. Find the first five terms of the sequence and write corresponding seri...

    Text Solution

    |