Home
Class 11
MATHS
Show that the middle term in the expansi...

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

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

Show that the middle term in the expansion of (x-1/x)^(2n) is (1.3.5.7....(2n-1))/(n!)(-2)^n

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

Show that the value of the middle term in the expansion of (x+(1)/(2x))^(2n)" is " (1.3.5.....(2n-1))/(n!)

The middle term in the expansion of (1-3x+3x^2-x^3)^(2n) is

Determine: nth term in the expansion of (x+1/x)^(2n)

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

Coefficient of x^n in the expansion of (1+x)^(2n) is

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

Show that the sum of the coefficients of the odd terms in the expansion of (1+x)^(2n)" is "2^(2n-1)

Show that the sum of the coefficient of first (r+1) terms in the expansions of (1-x)^(-n) is ((n+1)(n+2)...(n+r))/(r!)

CENGAGE PUBLICATION-BINOMIAL THEOREM-All Questions
  1. If the sum of coefficient of first half terms in the expansion of (x+y...

    Text Solution

    |

  2. Find the value of underset(p=1)overset(n)sum(underset(m=p)overset(n)su...

    Text Solution

    |

  3. Show that the middle term in the expansion of (x+1)^(2n) is (1.3.5.......

    Text Solution

    |

  4. If the middle term in the expansion of (x^2+1//x)^n is 924 x^6 , then...

    Text Solution

    |

  5. The first three terms in the expansion of (1+a x)^n(n!=0) are 1,6x and...

    Text Solution

    |

  6. If x^4 occurs in the rth term in the expansion of (x^4+1/(x^3))^(15), ...

    Text Solution

    |

  7. Find the coefficient of x^(-10) in the expansion of (a/x+b x)^(12) .

    Text Solution

    |

  8. Find the constant term in the expansion of (x-1/x)^6dot

    Text Solution

    |

  9. If the coefficients of (r-5) th and(2r-1) th terms in the expansion of...

    Text Solution

    |

  10. In ( 2^(1/3)+1/3^(1/ 3))^n if the ratio of 7th term from the beginnin...

    Text Solution

    |

  11. If the coefficient of 4th term in the expansion of (a+b)^n is 56, then...

    Text Solution

    |

  12. If p and q are positive, then prove that the coefficients of x^p and x...

    Text Solution

    |

  13. Find the number of irrational terms in the expansion of (5^(1//6)+2^(1...

    Text Solution

    |

  14. If x^p occurs in the expansion of (x^2+1/x)^(2n) , prove that its coef...

    Text Solution

    |

  15. The co-efficient of a^(3)b^(4)c^(5) in the expansion of (bc+ca+ab)^(6)...

    Text Solution

    |

  16. The coefficient of x^7 in the expansion of (1-x-x^2+x^3)^6 is

    Text Solution

    |

  17. If the number of terms in the expansion of (x+y+z)^n are 36, then find...

    Text Solution

    |

  18. The coefficient of a^3b^4c in the expansion of (1+a-b+c)^9 is equal to

    Text Solution

    |

  19. The coefficient of x^4 in the expansion of (1+x+x^2+x^3)^11 is

    Text Solution

    |

  20. Find the number of terms which are free from radical signs in the e...

    Text Solution

    |