Home
Class 11
MATHS
If (1+x)^n=c0+c1x+c2x^2+....+cnx^n,then ...

If `(1+x)^n=c_0+c_1x+c_2x^2+....+c_nx^n`,then show that `c_0/1+c_2/3+c_4/5+...=2^n/(n+1)`

Promotional Banner

Topper's Solved these Questions

  • MODEL QUESTION PAPERS-SET 10

    UNITED BOOK HOUSE|Exercise EXERCISE|48 Videos

  • MODEL QUESTION PAPERS-SET 12

    UNITED BOOK HOUSE|Exercise EXERCISE|49 Videos

Similar Questions

Explore conceptually related problems

If (1+x)^n=C_0+C_1x+C_2x^2+…..+C_nx^n .then show that C_1+2C_2+…. nC_n=n.2^(n-1) .

If (1+x)^n=C_0+C_1x+C_2x^2+.......+C_n x^n , then show that the sum of the products of the coefficients taken two at a time, represented by sumsum_(0lt=iltjlt=n) ""^nc_i ""^n c_j is equal to 2^(2n-1)-((2n)!)/ (2(n !)^2)

If (1+x)^(n)=C_(0)+C_(1)x+C_(2)x^(2)+.....+C_(n)x^(n) then show : C_(1)-2C_(2)+3C_(3)-....+(-1)^(n-1)n.C_(n)=0

If (1+x)^(n)=C_(0)+C_(1)x+C_(2)x^(2)+.....+C_(n)x^(n) then show : (C_(0))/(1)+(C_(2))/(3)+(C_(4))/(5)+....=(2^(n))/(n+1)

If (1+x)^(n)=C_(0)+C_(1)x+C_(2)x^(2)+.....+C_(n)x^(n) then show : (C_(0))/(1)+(C_(1))/(2)+(C_(2))/(3)+......+(C_(n))/(n+1)=(2^(n+1)-1)/(n+1)

If (1+x)^(n)=C_(0)+C_(1)x+C_(2)x^(2)+.....+C_(n)x^(n) then show : (C_(0))/(1)-(C_(1))/(2)+(C_(2))/(3)-......+(-1)^(n).(C_(n))/(n+1)=(1)/(n+1)

If (1+x)^(n)=C_(0)+C_(1)x+C_(2)x^(2)+.....+C_(n)x^(n) then show : 3.^(n)C_(0)-8.^(n)C_(1)+13.^(n)C_(2)-18.^(n)C_(3)+....."up to"(n+1)"terms" =0

If (1+x)^(n)=C_(0)+C_(1)x+C_(2)x^(2)+.....+C_(n)x^(n) then show : C_(1)+2.C_(2)+3.C_(3)+....+n.C_(n)=n.2^(n-1)

If (1+x)^n=C_0+C_1x+C_2 x^2+...+C_n x^n , n in N ,then C_0-C_1+C_2-.....+(-1)^(n-1)C_(m-1), is equal to (mltn)

If (18x^2+12x+4)^n = a_0 +a_(1x)+ a_(2x)^2 +......+ a_(2n)x^(2n) , prove that a_r= 2^n3^r ( "^(2n)C_r + "^(n)C_1 "^(2n-2)C_r + "^(n)C_2 "^(2n-4)C_r + ....

UNITED BOOK HOUSE-MODEL QUESTION PAPERS-SET 11-EXERCISE
  1. Prove by mathematical induction. 1.1! + 2. 2! + 3. 3! + ... +n . n! = ...

    Text Solution

    |

  2. If z = x + iy then l z - 8| + Iz + 8| = 20. represents a ellipse

    Text Solution

    |

  3. If (1+x)^n=c0+c1x+c2x^2+....+cnx^n,then show that c0/1+c2/3+c4/5+...=2...

    Text Solution

    |

  4. If the ath and bth term of an AP are 1/b and 1/a,then show that (ab)th...

    Text Solution

    |

  5. In /\XYZthe co-ordinate of Y and Z are (-a, 0) and (a, 0), andangle XZ...

    Text Solution

    |

  6. If the three straight lines ax + 2y + 1 = 0, 3y + bx + 1 = 0 and cx+ 4...

    Text Solution

    |

  7. If the circles x^2+y^2+2ax+c^2=0and x^2+y^2+2by+c^2=0touch each other,...

    Text Solution

    |

  8. Find the co-ordinate of a point equidistance from the points' (0, 0. 0...

    Text Solution

    |

  9. Prove that lim(xrarr1)(x^2-sqrtx)/(sqrtx-1)=3

    Text Solution

    |

  10. Prove that sqrt5 is irrational, (use the method of contradiction).

    Text Solution

    |

  11. In xy plane, |x — y | = 1 represents an equation of a circle and one d...

    Text Solution

    |

  12. Find the mean diaviation with respect to median of the frequency dist...

    Text Solution

    |

  13. If (acosthetasecphi-x)/(asin(theta+phi))=(y-bsinthetasecphi)/(bcos(th...

    Text Solution

    |

  14. If sinalpha+sinbeta=1/2,cosalpha+cosbeta=5/4find the value of tanalpha...

    Text Solution

    |

  15. Solve :(x+1)(x+2)(x+3)(x+4)=120

    Text Solution

    |

  16. In a polygon, the mesurement of least internal angle is 120^@. If thea...

    Text Solution

    |

  17. Out of 15 boys, 7 are skaut. In how mariy different way can 12 boys be...

    Text Solution

    |

  18. Draw the graph of the following system of inequation and show the comm...

    Text Solution

    |

  19. Find the equation of a parabola having the co-ordinate,of vertex is (-...

    Text Solution

    |

  20. Find the equation of an ellipse having vertices (-1, 2)- and (9, 2) . ...

    Text Solution

    |