Home
Class 11
MATHS
The coefficient of x^n, where n is any p...

The coefficient of `x^n`, where n is any positive integer, in the expansion of `(1+2x+3x^2 +... to oo)^(1//2)` is:

A

1

B

`(n+1)/2`

C

`2n+1`

D

`n+1`.

Text Solution

Verified by Experts

Promotional Banner

Topper's Solved these Questions

  • BINOMIAL THEOREM

    MODERN PUBLICATION|Exercise EXERCISE|221 Videos

  • COMPLEX NUMBERS

    MODERN PUBLICATION|Exercise EXERCISE|291 Videos

Similar Questions

Explore conceptually related problems

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

Find the coefficient of the term involving x^2 in the expansion of (3x-1/x)^6 .

In the expansion of (x^(2) + 1 + (1)/(x^(2)))^(n), n in N ,

If the coefficient of the rth, (r+1)th and (r+2)th terms in the expansion of (1+x)^(n) are in A.P., prove that n^(2) - n(4r +1) + 4r^(2) - 2=0 .

Find the coefficient of (A) x^9 (B) the term independent of x in the expansion of (x^2 - 1/(3x))^9 .

Show 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) .

If|x|<1, then the coefficient of x^6 in the expansion of (1+x + x^2)^-3 is:

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)

The coefficient of x^17 in the expansion of : (x-1)(x-2)(x-3) ...... (x-18) is :

MODERN PUBLICATION-BINOMIAL THEOREM-EXERCISE
  1. Find 'a' if the coefficients of x^(2) and x^(3) in the expanion of (3 ...

    Text Solution

    |

  2. Using binomial theorem. the value of (0.999)^3,correct to 3 decimal pl...

    Text Solution

    |

  3. The coefficient of x^n, where n is any positive integer, in the expans...

    Text Solution

    |

  4. If ""^(2n+1)P(n-1): ""^(2n-1)Pn =3:5 then the value of n equals :

    Text Solution

    |

  5. If|x|<1, then the coefficient of x^6 in the expansion of (1+x + x^2)^-...

    Text Solution

    |

  6. ""^15C0.""^5C5+""^15C1.""^5C4+""^15C2.""^5C3+ ""^15C3.^5C2+""^15C4.""^...

    Text Solution

    |

  7. Every body in a room shakes hand with every body else. The total numbe...

    Text Solution

    |

  8. ""^15C8+""^15C9-""^15C6-""^15C7=

    Text Solution

    |

  9. If the rth term in the expansion of (x/3-2/x^2)^10 contains x^4, then ...

    Text Solution

    |

  10. If 5^(99) is divided by 13, the remainder is

    Text Solution

    |

  11. The total number of terms in the expansion of (x+y)^100 after simplifi...

    Text Solution

    |

  12. If Pm stands for ""^mPm, then : 1+1.P1+2P2+3P3+.........+nPn is equal...

    Text Solution

    |

  13. The number of positive integers satisfying the inequality ""^(n+1)C(n-...

    Text Solution

    |

  14. The number of diagonals of a polygon of 20 sides is :

    Text Solution

    |

  15. he number of ways in which 5 boys and 5 girls can be seated for a phot...

    Text Solution

    |

  16. (""^8C0)/6-""^8C1+""^8C2 .6-""^8C3 .6^2+....+ ""^8C8 .6^7 =

    Text Solution

    |

  17. What is the smallest natural number n such that n ! is divisible by 99...

    Text Solution

    |

  18. What is the number of words formed from the letters of the word ‘JOKE’...

    Text Solution

    |

  19. Find the coefficient indepandent of x in the expansion of (1 + x +...

    Text Solution

    |

  20. The number of ways in which 6 men and 5 women can sit at a round table...

    Text Solution

    |