Home
Class 11
MATHS
Find the coefficient of x^k in1+(1+x)+(1...

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

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

Find the coefficient of x^n in the expansion of (1+x)(1+x)^ndot

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

Find the coefficient of x^n in the expansion of (1-9x+20 x^2)^(-1)dot

Find the coefficient of x^r in the expansion of 1 +(1 + x) + (1 + x)^2 +.......+ (1 + x)^n .

If n is a positive integer, find the coefficient of x^(-1) in the expansion of (1+x)^n(1+1/x)^ndot

The coefficient of x^(n) in (x+1)/((x-1)^(2)(x-2)) is

Find the coefficient of x^5 in the expansion of (1+x)^(21)+(1+x)^(22)+.........+(1+x)^(30)dot

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

Find the coefficient of x^n in (1+x/(1!)+(x^2)/(2!)+........+(x^n)/(n !))^2 .

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

CENGAGE ENGLISH-BINOMIAL THEOREM-All Questions
  1. Find the coefficient of x^(50) in the expansion of (1+x)^(101)xx(1-x+x...

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

  9. If p+q=1, then show that sum(r=0)^n r^2^n Crp^r q^(n-r)=n p q+n^2p^2do...

    Text Solution

    |

  10. If (18 x^2+12 x+4)^n=a0+a(1x)+a2x2++a(2n)x^(2n), prove that ar=2^n3^r(...

    Text Solution

    |

  11. Prove that ^m C1^n Cm-^m C2^(2n)Cm+^m C3^(3n)Cm-=(-1)^(m-1)n^mdot

    Text Solution

    |

  12. Prove that "^n C0^(2n)Cn-^n C1^(2n-1)Cn+^n C2xx^(2n-2)Cn++(-1)^n^n Cn^...

    Text Solution

    |

  13. Find the sum sum(r=0)^n^(n+r)Cr .

    Text Solution

    |

  14. Find the value of sumsum(0leilejlt=n)(i+j)(nCi+n Cj)dot

    Text Solution

    |

  15. Find the value of sumsum(0leilejlt=n)ci^n"" cj^ndot

    Text Solution

    |

  16. Find the value of underset(0leiltjlen)(sumsum)(.^(n)C(i)+.^(n)C(j)).

    Text Solution

    |

  17. Find the sum sumsum(0leiltjlen) "^nCi"^nCj

    Text Solution

    |

  18. Prove that sum(r=0)^ssum(s=1)^n^n Cs^n Cr=3^n-1.

    Text Solution

    |

  19. Find the sum sumsum(0leiltjlen)"^nCi

    Text Solution

    |

  20. Find the coefficient of x^4 in the expansion of (x/2-3/x^2)^10.

    Text Solution

    |