Home
Class 12
MATHS
Prove that the coefficient of the middle...

Prove that the coefficient of the middle term in the expansion of `(1+x)^(2n)` is equal to the sum of the coefficients of middle terms in the expansion of `(1+x)^(2n-1)`

Promotional Banner

Topper's Solved these Questions

  • Binomial Theorem for Positive Integrel Index

    A DAS GUPTA|Exercise Exercise|113 Videos

  • Application of dy/dx

    A DAS GUPTA|Exercise Exercise|45 Videos

  • Circles

    A DAS GUPTA|Exercise EXERCISE|122 Videos

Similar Questions

Explore conceptually related problems

Show that the coefficient of the middle term in the expansion of (1+x)^(2n) is equal to the sum of the coefficients of two middle terms in the expansion of (1+x)^(2n-1)

Show that the coefficient of middle term in the expansion of (1 + x)^(20) is equal to the sum of the coefficients of two middle terms in the expansion of (1 + x)^(19) .

Write the coefficient of the middle term in the expansion of (1+x)^(2n) .

Find the sum of the coefficient of to middle terms in the binomial expansion of (1+x)^(2n-1)

Find the middle term in the expansion of (1+x)^(2n)

The ratio of the coefficient of the middle term in the expansion of (1+x)^(20) and the sum of the coefficients of two middle terms in expansion of (1+x)^(19) is _____ .

The middle terms in the expansion of (1+x)^(2n+1) is (are)

ii) Show that the coefficient of the middle term in theexpansion of (1+x)^(40) is equal to the sum of thecoefficients of two middle terms of (1+x)^(39)

A DAS GUPTA-Binomial Theorem for Positive Integrel Index-Exercise
  1. If in any binomial expansion a, b, c and d be the 6th, 7th, 8th and 9t...

    Text Solution

    |

  2. The value of x in the expression (x+x^((log)(10)))^5 if third term in ...

    Text Solution

    |

  3. Prove that the coefficient of the middle term in the expansion of (1+x...

    Text Solution

    |

  4. In the expansion of (1 + x)^43 ,the co-efficients of (2r + 1)th and (r...

    Text Solution

    |

  5. Prove that in the expansion of (1+x)^(2n), the coefficient of x^n is d...

    Text Solution

    |

  6. The coefficient of 5th, 6th and 7th terms in the expansion of (1+x)^n ...

    Text Solution

    |

  7. Given positive integers r>1,n> 2, n being even and the coefficient of...

    Text Solution

    |

  8. If the coefficients of three consecutive terms in the expansion of (1 ...

    Text Solution

    |

  9. If a,b,c be the three consecutive coefficients in the expansion of a p...

    Text Solution

    |

  10. If a,b,c and d are any four consecutive coefficients in the expansi...

    Text Solution

    |

  11. If a,b,c and d are any four consecutive coefficients in the expansi...

    Text Solution

    |

  12. If the four consecutive coefficients in any binomial expansion be a, b...

    Text Solution

    |

  13. Let (1+x^2)^2*(1+x)^n=sum(k=0)^(n+4)ak*x^k If a1, a2 and a3 are iun ...

    Text Solution

    |

  14. If n be a positive integer then prove that the integral part P of (5+2...

    Text Solution

    |

  15. If (9+4sqrt5)^n=p+beta where n and p are positive integers and beta is...

    Text Solution

    |

  16. Integer just greater tehn (sqrt(3)+1)^(2n) is necessarily divisible by...

    Text Solution

    |

  17. The greatest coefficient in the expansion of (1+x)^(2n) is

    Text Solution

    |

  18. If x=1//3, find the greatest tem in the expansion of (1+4x)^8dot

    Text Solution

    |

  19. Find the numerically greatest term in the expansion of (3-2x)^9 when x...

    Text Solution

    |

  20. Find the value of the greatest term in the expansion of sqrt3(1+frac{1...

    Text Solution

    |