Home
Class 11
MATHS
Prove that the term independent of x in ...

Prove that the term independent of x in the expansion of `(x +1/x)^(2n)` is `{1 . 3 . 5.....(2n-1)}/(n!).2^n`

Text Solution

Verified by Experts

N/a
Promotional Banner

Topper's Solved these Questions

  • BINOMIAL THEOREM

    NAGEEN PRAKASHAN|Exercise Exercise 8D|8 Videos

  • BINOMIAL THEOREM

    NAGEEN PRAKASHAN|Exercise Exercise 8E|20 Videos

  • BINOMIAL THEOREM

    NAGEEN PRAKASHAN|Exercise Exercise 8B|38 Videos

  • COMPLEX NUMBERS AND QUADRATIC EQUATION

    NAGEEN PRAKASHAN|Exercise MISCELLANEOUS EXERCISE|20 Videos

Similar Questions

Explore conceptually related problems

Prove that the term independent of x in the expansin of (x+(1)/(x))^(2n) is (1.3.5(2n-1))/(n!)*2^(n)

The term independent of x in the expansion of (1+x)^(n)(1-(1)/(x))^(n) is

if the term independent of x in the expansion (2x-(1)/(x))^(n) is -160, find n

n th term in the expansion of (x+(1)/(x))^(2n)

Prove that the middle term in the expansion of (x+ 1/x)^(2n) is (1.3.5…(2n-1)/(n! 2^n

The middle term in the expansion of (x+(1)/(2x))^(2n) is -

Let P_(n)=((1+x)(1-x^(2))(1+x^(3))(1-x^(4)))/({(1+x)(1-x^(2))(1+x^(3))(1-x^(4))(1-x^(2n))}^(2)) Let Prove that the term independent of x in the expansion of (x^(2)+(1)/(x^(2))+2)^(2n) is equal to lim_(x rarr-1)Pn.

Coefficient of the term independent of x in the expansion of (1+x)^(2n)(x/(1-x))^(-2n) is:

NAGEEN PRAKASHAN-BINOMIAL THEOREM-Exercise 8C
  1. Find the coefficient of x^(2).y^(7) in the expansion of (x+2y)^(9)

    Text Solution

    |

  2. Prove that the ratio of the coefficient of x^10 in (1 - x^2)^10 & the ...

    Text Solution

    |

  3. Prove that the greatest coefficient in the expansion of (1+x)^(2n) is...

    Text Solution

    |

  4. Find a positive value of m for which the coefficient of x^2 in the ex...

    Text Solution

    |

  5. The sum of the coefficients of x^(32) and x^(-17) in (x^4- 1/(x^3))^15...

    Text Solution

    |

  6. If the coefficient of x^7 in (ax^2+1/(bx))^11 is equal to the coeffici...

    Text Solution

    |

  7. Find the coefficient of x^9 in the expansion of (x^2-1/(3x))^9.

    Text Solution

    |

  8. Find the coefficient of x^(10) in the expansion of (1-x^(2))^(10)

    Text Solution

    |

  9. The coefficient of x^(-17) in the expansion of (x^4-1/x^3)^(15) is

    Text Solution

    |

  10. Find the coefficient of x^(40) in the expansion of (1+2x+x^2)^(27)dot

    Text Solution

    |

  11. If 'n' is a positive integer then prove that the coefficient fox^(m) i...

    Text Solution

    |

  12. Find the term independent of x (constant term) in the following expans...

    Text Solution

    |

  13. Prove that the term independent of x in the expansion of (x +1/x)^(2n)...

    Text Solution

    |

  14. Find the coefficient of a^5b^7in(a-2b)^(12)

    Text Solution

    |

  15. Find the coefficient of x^(2).y^(7) in the expansion of (x+2y)^(9)

    Text Solution

    |

  16. Prove that the ratio of the coefficient of x^10 in (1 - x^2)^10 & the ...

    Text Solution

    |

  17. prove that the coefficient of x^n in the expansion of (1+x)^(2n) is tw...

    Text Solution

    |

  18. Find a positive value of m for which the coefficient of x^2 in the ex...

    Text Solution

    |

  19. The sum of the coefficients of x^(32) and x^(-17) in (x^4- 1/(x^3))^15...

    Text Solution

    |

  20. Find the coefficients of x^7 in (a x^2+1/(b x))^(11)a n dx^(-7)in(a x^...

    Text Solution

    |