Home
Class 11
MATHS
If |x|<1, then find the coefficient of x...

If `|x|<1,` then find the coefficient of `x^n` in the expansion of `(1+x+x^2+......)^2dot`

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

If f(x) = |(x + lamda,x,x),(x,x + lamda,x),(x,x,x + lamda)|, " then " f(3x) - f(x) =

If f(x) = |(1,x,x+1),(2x,x(x-1),x(x+1)),(3x(x-1),x(x-1)(x-2),x(x+1)(x-1))| , using properties of determinant, find f(2x) - f(x).

If x is a negative integer, then (a) x+|x|=0 (b) x-|x|=0 x+|x|=-2x (d) x=-|x|

If x is a positive integer, then (a) x+|x|=0 (b) x-|x|=0 (c) x+|x|=-2x (d) x=-1|x|

If x is a negative integer, then (a) x+|x|=0 (b) x-|x|=0 (c) x+|x|=-2x (d) x=-|x|

If f(x)=sgn(x)={(|x|)/x,x!=0, 0, x=0 and g(x)=f(f(x)), then at x=0,g(x) is

If {x} and [x] represent fractional and integral part of x respectively then solve the equation x-1=(x-[x])(x-{x})

Solve the following : (i) |x-2|=(x-2) " (ii) " |x+3| = -x-3 (iii) |x^(2)-x|=x^(2)-x " (iv) " |x^(2)-x-2| =2+x-x^(2)

If f(x)=|[x-2, (x-1)^2, x^3] , [(x-1), x^2, (x+1)^3] , [x,(x+1)^2, (x+2)^3]| then coefficient of x in f(x) is

If f(x)= |1 x x+1 2x x(x-1)(x+1)x3x(x-1)x(x-1)(x-2)(x+1)x(x-1)| then f(500) is equal to a. 0 b. 1 c. 500 d. -500

CENGAGE ENGLISH-BINOMIAL THEOREM-All Questions
  1. If |x|<1, then find the coefficient of x^n in the expansion of (1+2x+3...

    Text Solution

    |

  2. If (r+1)t h term is the first negative term in the expansion of (1+x)^...

    Text Solution

    |

  3. If |x|<1, then find the coefficient of x^n in the expansion of (1+x+x^...

    Text Solution

    |

  4. If |x|>1, then expand (1+x)^(-2)dot

    Text Solution

    |

  5. Find the cube root of 217, correct to two decimal places.

    Text Solution

    |

  6. Find the coefficient of x^2 in (a/(a+x))^(1//2)+(a/(a-x))^(1//2)

    Text Solution

    |

  7. Prove that ^10 C1(x-1)^2-^(10)C2(x-2)^2+^(10)C3(x-3)^2+-^(10)C(10)(x-1...

    Text Solution

    |

  8. If the third term in the expansion of (1+x)^mi s-1/8x^2, then find the...

    Text Solution

    |

  9. Prove that sum(r=0)^n r(n-r)(^nC r)^2=n^2(^(2n-2)Cn)dot

    Text Solution

    |

  10. Prove that 1-^n C1(1+x)/(1+n x)+^n C2(1+2x)/((1+n x)^2)-^n C3(1+3x)/((...

    Text Solution

    |

  11. Find the coefficient of x^(20) in (x^2+2+1/(x^2))^(-5)(1+x^2)^(40)dot

    Text Solution

    |

  12. The number of terms in the expansion of (a+b+c)^n , where n in Ndot

    Text Solution

    |

  13. Find the coefficient of x^(50) in the expansion of (1+x)^(101)xx(1-x+x...

    Text Solution

    |

  14. Find the coefficient of x^4 in the expansion of (2-x+3x^2)^6dot

    Text Solution

    |

  15. Find the coefficient of x^k in1+(1+x)+(1+x)^2++(1+x)^n(0lt=klt=n)dot

    Text Solution

    |

  16. Find the term independent of x in the expansion of (1+x+2x^3)[(3x^2//...

    Text Solution

    |

  17. If aa n db are distinct integers, prove that a-b is a factor of a^n-b^...

    Text Solution

    |

  18. Find the a ,b ,a n dn in th expansion of (a+b)^n if the first three te...

    Text Solution

    |

  19. Find the coefficient of x^(25) in expansion of expression sum(r=0)^(50...

    Text Solution

    |

  20. If the sum of the coefficients of the first, second, and third terms ...

    Text Solution

    |