Home
Class 12
MATHS
Prove that sqrt(C1) +sqrt(C2) +sqrt(C3)+...

Prove that `sqrt(C_1) +sqrt(C_2) +sqrt(C_3)+...+sqrt(C_n)le 2^(n-1) +(n-1)/2`

Promotional Banner

Topper's Solved these Questions

  • BINOMIAL THEOREM

    MOTION|Exercise Exercise -4 (Level - I) ( Previous Year )|12 Videos

  • BINOMIAL THEOREM

    MOTION|Exercise Exercise -4 (Level - II) ( Previous Year )|7 Videos

  • BINOMIAL THEOREM

    MOTION|Exercise Exercise - 2 (Level - II) (Multiple Correct ) (MIXED PROBLEMS )|3 Videos

  • BASIC MATHEMATIC & LOGARITHM

    MOTION|Exercise Exercise - 4|4 Videos

  • CIRCLE

    MOTION|Exercise Exercise - 4 | Level - II (Previous Year | JEE Advanced|22 Videos

Similar Questions

Explore conceptually related problems

If C_(r ) = (n!)/(r!(n - r)!) , then prove that sqrt(C_(1)) + sqrt(C_(2)) + …. + sqrt(C_(n)) sqrt(n(2^(n) - 1))

Prove that (sqrt(2)-1)^(2n)

If C_r=(n !)/([r !(n-r)]), the prove that sqrt(C_1)+sqrt(C_2)+.......sqrt(C_n) lt sqrt(n(2^n-1)) ="">

If (1+x)^n = C_0 + C_1x + C_2x^2 + ………. + C_n x^n , prove that : C_0 + (C_1)/(2) + (C_2)/(3) + ……. + (C_n)/(n+1) = (2^(n+1) -1)/(n+1)

If a_(1),a_(2),a_(3)... are in A.P then prove that (1)/(sqrt(a)_(1)+sqrt(a)_(2))(+)/(sqrt(a)_(2)+sqrt(a)_(3))+...+(1)/(sqrt(a)_(n-1)+sqrt(a)_(n))=(n-1)/(sqrt(a)_(n)+sqrt(a)_(1))

Prove that C_0+(C_1)/(2)+(C_2)/(3)+....+(C_n)/(n+1)=(2^(n+1)-1)/(n+1)

Prove that 1+(1)/(sqrt2)+(1)/(sqrt3)+....+(1)/(sqrtn) ge sqrtn, AA n in N

The value of lim_(n rarr oo)(sqrt(1)+sqrt(2)+sqrt(3)+....+2sqrt(n))/(n sqrt(n)) is

If (1+a)^(n)=.^(n)C_(0)+.^(n)C_(1)a+.^(n)C_(2)a^(2)+ . . +.^(n)C_(n)a^(n) , then prove that .^(n)C_(1)+2.^(n)C_(2)+3.^(n)3C_(3)+ . . .+n.^(n)C_(n)=n.2^(n-1) .

If (1 + x)^(n) = C_(0) + C_(1) x + C_(2) x^(2) + C_(3) x^(3) + … + C_(n) x^(n) , prove that C_(0) - (C_(1))/(2) + (C_(2))/(3) -…+ (-1)^(n) (C_(n))/(n+1) = (1)/(n+1) .

MOTION-BINOMIAL THEOREM -Exercise -3 ( Subjective )
  1. prove that : C0^2+3C1^@+5C2^2+...+(2n+1)Cn^2=((n+1)2n!)/(n!)^2

    Text Solution

    |

  2. If (1 + x)^(n) = C(0) = C(1) x + C(2) x^(2) + …+ C(n) x^(n) , find...

    Text Solution

    |

  3. Prove that sqrt(C1) +sqrt(C2) +sqrt(C3)+...+sqrt(Cn)le 2^(n-1) +(n-1)/...

    Text Solution

    |

  4. If C(r ) = (n!)/(r!(n - r)!), then prove that sqrt(C(1)) + sqrt(C(2)...

    Text Solution

    |

  5. Sum of all the digits of the coefficient of x^(5) in the expansion of ...

    Text Solution

    |

  6. Find the coefficient of x^(4) in the expansion of (1+x+x^(2)+x^(3))^(1...

    Text Solution

    |

  7. Find the coefficients of x^(4) in the expansions of (2 - x + 3x^(2...

    Text Solution

    |

  8. Let a = (72!)/(36!)^2-1 , then (A) a is odd (B) a is divisible by 7...

    Text Solution

    |

  9. find the sum of the series sum(r=0)^n(-1)^r *"^nCr[1/(2^r)+(3^r)/(2^(...

    Text Solution

    |

  10. Given that (1+x+x^2)^n=a0+a1x+a2x^2+........+a(2n)x^(2n) find the val...

    Text Solution

    |

  11. Given that (1+x+x^(2))^(n)=a(0)+a(1)x+a(2)x^(2)+......+a(2n)x^(2n), f...

    Text Solution

    |

  12. Given that (1+x+x^(2))^(n)=a(0)+a(1)x+a(2)x^(2)+......+a(2n)x^(2n), f...

    Text Solution

    |

  13. If n(j(r))=((1-xn)(1-x(n-1))(1-x^(n-2)).......(1-x^(n-r+1)))/((1-x)(1-...

    Text Solution

    |

  14. Prove that sum(k=0)^n ^nCk sinKx.cos(n-K)x=2^(n-1)sin nx

    Text Solution

    |

  15. The expressions 1+x,1+x+x^2,1+x+x^2+x^3.............1+x+x^2+.............

    Text Solution

    |

  16. Find the coefficients of x^(6) in the expansion of (ax^(2) + bx +...

    Text Solution

    |

  17. Find the coefficient of x^2 y^3 z^4 in the expansion of (ax-by+cz)^9

    Text Solution

    |

  18. Find the coefficient of x^2 y^3 z^4 in the expansion of (ax -by +cx...

    Text Solution

    |

  19. If sum(r=0)^(2n)ar(x-2)^r=sum(r=0)^(2n)br(x-3)^ra n dak=1 for all kgeq...

    Text Solution

    |

  20. Show that the integral part in each of the following is odd. n in N. ...

    Text Solution

    |