Home
Class 11
MATHS
The coefficient of 1//x in the expansion...

The coefficient of `1//x` in the expansion of `(1+x)^n(1+1//x)^n` is (a).`(n !)/((n-1)!(n+1)!)` (b). `((2n)!)/((n-1)!(n+1)!)` (c). `((2n)!)/((2n-1)!(2n+1)!)` (d). none of these

Text Solution

AI Generated Solution

Promotional Banner

Topper's Solved these Questions

  • COMPLEX NUMBERS AND QUADRATIC EQUATIONS

    CENGAGE ENGLISH|Exercise All Questions|886 Videos

Similar Questions

Explore conceptually related problems

The coefficient of 1//x in the expansion of (1+x)^n(1+1//x)^n is (n !)/((n-1)!(n+1)!) b. ((2n)!)/((n-1)!(n+1)!) c. ((2n)!)/((2n-1)!(2n+1)!) d. none of these

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

The coefficients fo x^(n) in the expansion of (1+x)^(2n) and (1+x)^(2n-1) are in the ratio

If x^m occurs in the expansion (x+1//x^2)^(2n) , then the coefficient of x^m is a. ((2n)!)/((m)!(2n-m)!) b. ((2n)!3!3!)/((2n-m)!) c. ((2n)!)/(((2n-m)/3)!((4n+m)/3)!) d. none of these

If |x|<1, then the coefficient of x^n in expansion of (1+x+x^2+x^3+)^2 is a. n b. n-1 c. n+2 d. n+1

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

If A and B are the coefficients of x^n in the expansion (1 + x)^(2n) and (1 + x)^(2n-1) respectively, then

If A and B are the coefficients of x^n in the expansion (1 + x)^(2n) and (1 + x)^(2n-1) respectively, then

The coefficient of x^(n) in the polynomial (x+""^(2n+1)C_(0))(X+""^(2n+1)C_(1)) (x+""^(2n+1)C_(2))……(X+""^(2n+1)C_(n)) is

(d^n)/(dx^n)(logx)=? (a) ((n-1)!)/(x^n) (b) (n !)/(x^n) (c) ((n-2)!)/(x^n) (d) (-1)^(n-1)((n-1)!)/(x^n)

CENGAGE ENGLISH-BINOMIAL THEOREM-All Questions
  1. If n and k are positive integers, show that 2^k( .^n C0)(.^n Ck)-2^(k-...

    Text Solution

    |

  2. Prove that (25)^(n+1)-24n+5735 is divisible by (24)^2 for all n=1,2,.....

    Text Solution

    |

  3. The coefficient of 1//x in the expansion of (1+x)^n(1+1//x)^n is (a).(...

    Text Solution

    |

  4. The coefficient x^5 in the expansion of (1+x)^(21)+(1+x)^(22)++(1+x)^...

    Text Solution

    |

  5. If x^m occurs in the expansion (x+1//x^2)^(2n) , then the coefficient ...

    Text Solution

    |

  6. If the coefficients of 5th, 6th , and 7th terms in the expansion of (1...

    Text Solution

    |

  7. If (1+2x+x^2)^n=sum(r=0)^(2n)ar x^r ,then ar is a.(.^nC2)^2 b. .^n ...

    Text Solution

    |

  8. In the expansion of (x^3-1/x^2)^n, n in N if sum of the coefficients o...

    Text Solution

    |

  9. If the coefficients of rth and (r+1)t h terms in the expansion of (3+7...

    Text Solution

    |

  10. In the expansion of (1+3x+2x^2)^6 , the coefficient of x^(11) is a. 14...

    Text Solution

    |

  11. If n-1Cr=(k^2-3)^nC(r+1), then (a) (-oo,-2] (b) [2,oo) (c) [-sqrt3, s...

    Text Solution

    |

  12. Prove that (3!)/(2(n+3))=sum(r=0)^n(-1)^r((^n Cr)/(^(r+3)Cr))

    Text Solution

    |

  13. If an=sum(r=0)^n1/(nCr), then sum(r=0)^n r/(nCr) equals

    Text Solution

    |

  14. The expression (x+((x^3-1)^(1/2))/2)^5+""(x-((x^3-1)^(1/2))/2)^5 is a ...

    Text Solution

    |

  15. Find ((dy) /dx) of sin(costheta) is

    Text Solution

    |

  16. In the binomial expansion of (a-b)^n,ngeq5, the sum of the 5th and 6t...

    Text Solution

    |

  17. Coefficient of x^(11) in the expansion of (1+x^2)^4(1+x^3)^7(1+x^4)^(...

    Text Solution

    |

  18. Given positive integers r gt 1, n gt 2 and that the coefficient of (3...

    Text Solution

    |

  19. The coefficient of x^4 in (x//2-3//x^2)^10 is a.(405)/(256) b. (504)/(...

    Text Solution

    |

  20. If Cr stands for nCr, then the sum of the series (2(n/2)!(n/2)!)/(n...

    Text Solution

    |