Home
Class 11
MATHS
prove that sum(r=0)^n(-1)^r^n Cr. [1/(...

prove that `sum_(r=0)^n(-1)^r^n C_r`. [`1/(2^r)+(3^r)/(2^(2r))+(7^r)/(2^(3r))+(15^r)/(2^(4r))+ `......up to m terms`]`= `(2^(m n)-1)/(2^(m n)(2^n-1))`

Promotional Banner

Topper's Solved these Questions

  • COMPLEX NUMBERS AND QUADRATIC EQUATIONS

    CENGAGE PUBLICATION|Exercise All Questions|877 Videos

Similar Questions

Explore conceptually related problems

Prove that (3!)/(2(n+3))=sum_(r=0)^n(-1)^r((n C_r)/((r+3)C_3))

If x+y=1, prove that sum_(r=0)^n .^nC_r x^r y^(n-r) = 1 .

Prove that sum_(r=0)^n r(n-r)(.^nC_ r)^2=n^2(.^(2n-2)C_n)dot

Prove that sum_(r=0)^(2n)(r. ^(2n)C_r)^2=n^(4n)C_(2n) .

Prove that sum_(r=1)^(n) tan^(-1) ((2^(r -1))/(1 + 2^(2r -1))) = tan^(-1) (2^(n)) - (pi)/(4)

The value of sum_(r=0)^(3n-1)(-1)^r .^(6n)C_(2r+1)3^r is

Prove that sum_(r=1)^n(-1)^(r-1)(1+1/2+1/3++1/r)(.^n C_r)=1/n .

Prove that sum_(r=1)^(m-1)(2r^2-r(m-2)+1)/((m-r)^m C_r)=m-1/mdot

If x + y = 1 , prove that sum_(r=0)^(n) r""^(n)C_(r) x^(r ) y^(n-r) = nx .

Prove that sum_(r=0)^(2n) r.(""^(2n)C_(r))^(2)= 2n.""^(4n-1)C_(2n-1) .

CENGAGE PUBLICATION-BINOMIAL THEOREM-All Questions
  1. The coefficient of x^(28) in the expansion of (1+x^(2)-x^(6))^(30) is

    Text Solution

    |

  2. The coefficient of x^(n) in (1+x)^(101) (1-x+x^(2))^(100) is nonzero, ...

    Text Solution

    |

  3. prove that sum(r=0)^n(-1)^r^n Cr. [1/(2^r)+(3^r)/(2^(2r))+(7^r)/(2^(...

    Text Solution

    |

  4. In the expansion of (7^(1//3)+11^(1//9))^(6561) ,

    Text Solution

    |

  5. If for z as real or complex, (1+z^2+z^4)^8=C0+C1z^2+C2z^4+...+C(16)z^(...

    Text Solution

    |

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

    Text Solution

    |

  7. if the 4^(th) term in the expansion of (ax+1)^(n) is 5//2, then

    Text Solution

    |

  8. Number of values of r satisfying the equation ,^69C(3r-1) -^(69)C(r^2)...

    Text Solution

    |

  9. If (4+sqrt(15))^n=I+f,where n is an odd natural number, I is an intege...

    Text Solution

    |

  10. In the expansion of (x+a)^n if the sum of odd terms is P and the sum o...

    Text Solution

    |

  11. If the coefficients of the rth, (r+1)t h ,(r-2)t h terms is the expans...

    Text Solution

    |

  12. The value/value of x in the expression (x+x^(log(10)x))^(5)if the thir...

    Text Solution

    |

  13. Let R=(5 sqrt 5+11)^(2n+1) and f=R-[R] where [] is the greatest intege...

    Text Solution

    |

  14. If |x| lt 1, then the coefficient of x^(n) in expansion of (1+x+x^(2)+...

    Text Solution

    |

  15. The coefficient of x^5in(1+2x+3x^2+)^(-3//2)i s(|x|<1)

    Text Solution

    |

  16. If x is so small that x^3 and higher powers of x may be neglected, the...

    Text Solution

    |

  17. If x is positive, the first negative term in the expansion of (1+x)^(2...

    Text Solution

    |

  18. Value of sum(k=1)^oosum(r=0)^k1/(3^k)(k Cr) is 2/3 b. 4/3 c. 2 d. 1

    Text Solution

    |

  19. If the expansion in powers of x of the function 1/[(1-a x)(1-b x)] is ...

    Text Solution

    |

  20. If f(x)=1-x+x^2-x^3+. . -x^(15)+x^(16)-x^(17) , then the coefficient o...

    Text Solution

    |