Home
Class 12
MATHS
If ( 1 + x ) ^(n) = a(0) + a (1) x + ...

If ` ( 1 + x ) ^(n) = a_(0) + a _(1) x + a_(2) x^(2) + ………. + a_(n)x^(n) ` , then show that
(i) ` a_(0) - a_(2) + a_(4) - a_(6) + ……… = 2^(n//2) cos . (npi)/4 `
(ii) ` a _(1) a_(3) + a_(5) - a_(7) + …….. = 2^(n//2) sin . (npi)/4 `

Promotional Banner

Topper's Solved these Questions

  • DEMOIVRE'S THEOREM

    AAKASH SERIES|Exercise ADDITIONAL EXERCISE|7 Videos

  • DEMOIVRE'S THEOREM

    AAKASH SERIES|Exercise EXERCISE -I|10 Videos

  • DEMOIVRE'S THEOREM

    AAKASH SERIES|Exercise EXERCISE - 6 (SHORT ANSWER QUESTIONS)|24 Videos

  • DEFINITE INTEGRALS

    AAKASH SERIES|Exercise Exercise (Level-2)|38 Videos

  • DIFFERENTIAL EQUATIONS

    AAKASH SERIES|Exercise Practice Exercise|62 Videos

Similar Questions

Explore conceptually related problems

a_(n) = n/(n+2) , a_(3) = ……….

a_(n) = 9-5n, a_(4) = ………….

a_(n) = 2^(n), a_(5) = ………

If (1+x+x^(2))^(n)=a_(0)+a_(1)x+a_(2)x^(2)+….+a_(2n)x^(2n) , then prove that a_(0)+a_(1)+a_(2)…..+a_(2n)=3^(n)

If (1+x+x^(2))^(n)=a_(0)+a_(1)x+a_(2)x^(2)+….+a_(2n)x^(2n) , then prove that a_(0)+a_(2)+a_(4)+……+a_(2n)=(3^(n)+1)/(2)

If (1+x+x^(2))^(n)=a_(0)+a_(1)x+a_(2)x^(2)+….+a_(2n)x^(2n) , then prove that a_(1)+a_(3)+a_(5)+….+a_(2n-1)=(3^(n)-1)/(2)

If (1+x+x^(2))^(n)=a_(0)+a_(1)x+a_(2)x^(2)+….+a_(2n)x^(2n) , then prove that a_(0)+a_(3)+a_(6)+a_(9)+……=3^(n-1)

a_(n) = (n-1) (n-2) then a_(2) = ……….

In an AP a_(1) = -4, a_(6)= 6 then a_(2) = …….

AAKASH SERIES-DEMOIVRE'S THEOREM-EXERCISE - 6 (LONG ANSWER QUESTIONS)
  1. If n is a positive integer, show that ( P + iQ)^(1//n) + ( P - iQ)^...

    Text Solution

    |

  2. If n is an integer then show that (1 + cos theta + i sin theta)^(n...

    Text Solution

    |

  3. If alpha, beta are the roots of the equation x^(2) - 2x + 4 = 0 the...

    Text Solution

    |

  4. If cos alpha+cos beta+cos gamma=0 & sin alpha +sin beta +sin gamma=0. ...

    Text Solution

    |

  5. If cos alpha+cos beta+cos gamma=0 & sin alpha +sin beta +sin gamma=0. ...

    Text Solution

    |

  6. If cos alpha + cos beta + cos gamma = 0 = sin alpha + sin beta + ...

    Text Solution

    |

  7. If cos alpha + cos beta + cos gamma = 0 = sin alpha + sin beta + ...

    Text Solution

    |

  8. If cos alpha + cos beta + cos gamma = 0 = sin alpha + sin beta + ...

    Text Solution

    |

  9. If cos alpha + cos beta + cos gamma = 0 sin alpha + sin beta + sin g...

    Text Solution

    |

  10. Solve the following equations. x^(4) - 1 = 0

    Text Solution

    |

  11. Solve the following equations. x^(5) + 1 = 0

    Text Solution

    |

  12. Solve the following equations. x^(4) + 1 = 0

    Text Solution

    |

  13. Solve the following equations x^(11)-x^7+x^4-1=0

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

  16. The common roots of the equation x^(12)-1=0,x^4+x^2+1=0 are

    Text Solution

    |

  17. Find the number of 15^(th)roots of unity, which are also 25^(th) roots...

    Text Solution

    |

  18. If z^(2) + z + 1 = 0, where z is a complex number , prove that ( z...

    Text Solution

    |

  19. If 1,alpha,alpha^2,alpha^3,…,alpha^(n-1) be the n^(th) roots of unity,...

    Text Solution

    |

  20. Prove the sum of 99t^(th) powers of the roots of the equation x^7-1 = ...

    Text Solution

    |