Home
Class 12
MATHS
Prove that sum(r=0)^n(-1)^r^n Cr[1/(2^r...

Prove that `sum_(r=0)^n(-1)^r^n C_r[1/(2^r)+3/(2^(2r))+7/(2^(3r))+(15)/(2^(4r))+ u ptomt e r m s]=(2^(m n)-1)/(2^(m n)(2^n-1))`

Promotional Banner

Topper's Solved these Questions

  • INVERSE TRIGONOMETRIC FUNCTIONS

    RESONANCE DPP|Exercise All Questions|15 Videos

  • MATRICES

    RESONANCE DPP|Exercise All Questions|7 Videos

Similar Questions

Explore conceptually related problems

Prove that sum_(r=0)^(n)(-1)^(r)nC_(r)[(1)/(2^(r))+(3)/(2^(2r))+(7)/(2^(3r))+(15)/(2^(4r))+...up to mterms]=(2^(mn)-1)/(2^(mn)(2^(n)-1))

Prove that sum_(r=0)^(n)r(n-r)C_(r)^(2)=n^(2)(^(2n-2)C_(n))

find the sum of the series 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 ]

Sigma_(r=0)^(n)(-1)^(r).^(n)C_(r)[(1)/(2^(r))+(3^(r))/(2^(2r))+...up rarr mterms ]

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

If sum_(r=0)^(n) (-1)^(r ).""^(n)C_(r)[(1)/(2^(r))+(3^(r))/(2^(2r))+(7^(r))/(2^(3r))+"……..""to m terms"] = k(1-1/(2^(mn))) , then k =

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

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

RESONANCE DPP-JEE MAINS-All Questions
  1. overset(pi)underset(-ip)int [cos px-sin qx]^(2) dx where p,q are integ...

    Text Solution

    |

  2. A forecast forr Indian team is to be made of the results of five crick...

    Text Solution

    |

  3. Prove that sum(r=0)^n(-1)^r^n Cr[1/(2^r)+3/(2^(2r))+7/(2^(3r))+(15)/(...

    Text Solution

    |

  4. If two events A and B are such that P(A^c)=0. 3. P(B)=0. 4a n dP(AnnB^...

    Text Solution

    |

  5. If four G.M.s are inserted between k1c and k2d , where k2=64 k1, then ...

    Text Solution

    |

  6. How many different nine digit numbers can be formed from the number 22...

    Text Solution

    |

  7. 18 points are indicated on the perimeter of a triangle ABC (see fig...

    Text Solution

    |

  8. If P(A)=0. 59 ,P(B)=0. 30P(AnnB)=0. 21 , then P(A^(prime)nnB^(prime)...

    Text Solution

    |

  9. A seven digit number is choosen. What the probability that even number...

    Text Solution

    |

  10. If the difference between mean and m0de is 63, the difference between ...

    Text Solution

    |

  11. A triangle ABC of area "Delta" is inscribed in the parabola y^2=4a x s...

    Text Solution

    |

  12. The algebraic sum of deviations of 10 observations measured from 16 is...

    Text Solution

    |

  13. 'A' writes a letter to his friend 'B' and gives it to his son to post ...

    Text Solution

    |

  14. The normal drawn at a point (a t1 2,-2a t1) of the parabola y^2=4a x m...

    Text Solution

    |

  15. 4 people are selected randomly out of six married couple. Find the ...

    Text Solution

    |

  16. Find the sum tantheta+1/2tantheta/2+1/(2^2)tantheta/(2^2)+1/(2^3)tanth...

    Text Solution

    |

  17. Match the column : 4 cards are selected from a pack of 52 playing card...

    Text Solution

    |

  18. The number of parabolas that can be drawn if two ends of the latus ...

    Text Solution

    |

  19. A class contains 4 boys and g girls. Every Sunday five students, inclu...

    Text Solution

    |

  20. Find the equation of the line passing through the point (2,3) and maki...

    Text Solution

    |