Home
Class 11
MATHS
If in the expansion of (1 + x)^n, the co...

If in the expansion of `(1 + x)^n`, the coefficients of pth and qth terms are equal, prove that `p+q=n+ 2`, where `p!=q`.

Text Solution

AI Generated Solution

Promotional Banner

Topper's Solved these Questions

  • ARITHMETIC PROGRESSIONS

    RD SHARMA ENGLISH|Exercise All Questions|248 Videos

  • BRIEF REVIEW OF CARTESIAN SYSTEM OF RECTANGULAR COORDINATES

    RD SHARMA ENGLISH|Exercise All Questions|77 Videos

Similar Questions

Explore conceptually related problems

In the expansion of (x^(2) + (1)/(x) )^(n) , the coefficient of the fourth term is equal to the coefficient of the ninth term. Find n and the sixth term of the expansion.

In in the expansion of (1+px)^(q) , q belongs to N , the coefficients of x and x^(2) are 12 and 60 respectively then p and q are

If the coefficients of (p+1) th and (P+3) th terms in the expansion of (1+x)^(2n) are equal then prove that n=p+1

Prove that he coefficient of x^n in the expansion of (1+x)^(2n) is twice the coefficient of x^(n) in the expansion of (1+x)^(2n-1)

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)

In an A.P., if p^(t h) term is 1/q and q^(t h) term is 1/p , prove that the sum of first pq terms is 1/2(p q+1), where p!=q .

Find out the sum of the coefficients in the expansion of the binomial (5p - 4q)^n , where n is a +ive integer.

In the expansion of (x+a)^n if the sum of odd terms is P and the sum of even terms is Q , then (a) P^2-Q^2=(x^2-a^2)^n (b) 4P Q=(x+a)^(2n)-(x-a)^(2n) (c) 2(P^2+Q^2)=(x+a)^(2n)+(x-a)^(2n) (d)none of these

prove that the coefficient of x^n in the expansion of (1+x)^(2n) is twice the coefficient of x^n in the expansion of (1+x)^(2n-1)

Prove that the coefficient of x^n in the expansion of (1+x)^(2n) is twice the coefficient of x^n in the expansion of (1+x)^(2n-1)

RD SHARMA ENGLISH-BINOMIAL THEOREM-All Questions
  1. If the coefficients of 5th, 6th , and 7th terms in the expansion of (1...

    Text Solution

    |

  2. If the coefficients of 2nd, 3rd and 4th terms in the expansion of (1...

    Text Solution

    |

  3. If in the expansion of (1 + x)^n, the coefficients of pth and qth term...

    Text Solution

    |

  4. Find a if the coefficients of x^2 and x^3 in the expansion of (3+a ...

    Text Solution

    |

  5. Find the coefficient of a^4 in the product (1+2a)^4(2-a)^5 using binom...

    Text Solution

    |

  6. In the expansion of (1+x)^n the binomial coefficients of three consecu...

    Text Solution

    |

  7. If in the expansion of (1+x)^n the coefficient of three consecutive te...

    Text Solution

    |

  8. If in any binomial expansion a, b, c and d be the 6th, 7th, 8th and 9t...

    Text Solution

    |

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

    Text Solution

    |

  10. If the 6th, 7th, 8th terms in the expansion of (x+ y)^n be 112, 7 and ...

    Text Solution

    |

  11. If the 2nd, 3rd and 4th terms in the expansion of (x+a)^n are 240, ...

    Text Solution

    |

  12. Find a, b and n in the expansion of (a+b)^n if the first three t...

    Text Solution

    |

  13. If p is a real number and if the middle term in the expansion of (p/2+...

    Text Solution

    |

  14. Write the number of terms in the expansion of (2+sqrt(3)x)^(10)+(2-sqr...

    Text Solution

    |

  15. Write the middle term in the expansion of ((2x^2)/3+3/(2x^2))^(10)dot

    Text Solution

    |

  16. Which term is independent of x in the expansion of (x-1/(3x^2))^9?

    Text Solution

    |

  17. If a\ a n d\ b denote respectively the coefficients of x^m a n d\ x^n ...

    Text Solution

    |

  18. Write the middle term in the expansion of (x+1/x)^(10)dot

    Text Solution

    |

  19. If a\ a n d\ b denote the sum of the coefficients in the expansions of...

    Text Solution

    |

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

    Text Solution

    |