Home
Class 12
MATHS
If n ge0 is integer, using induction met...

If `n ge0` is integer, using induction method prove that,
`(1)/(1+x)+(2)/(1+x^(2))+(4)/(1+x^(4))+...+(2^(n))/( 1+x^(2n))=(1)/(x-1)+(2^(n+1))/(1-x^(2^(n+1)))`.

Promotional Banner

Topper's Solved these Questions

  • MISCELLANEOUS EXAMPLES

    CHHAYA PUBLICATION|Exercise COORDINATE GEOMETRY (TWO DIMENSIONAL COORDINATE GEOMETRY)|124 Videos

  • MISCELLANEOUS EXAMPLES

    CHHAYA PUBLICATION|Exercise COORDINATE GEOMETRY (THREE DIMENSIONAL COORDINATE GEOMETRY)|10 Videos

  • MISCELLANEOUS EXAMPLES

    CHHAYA PUBLICATION|Exercise TRIGONOMETRY|148 Videos

  • METHOD OF SUBSTITUTION

    CHHAYA PUBLICATION|Exercise Sample Questions for Competitive Examination (Assertion-Reason Type)|2 Videos

  • ORDER AND DEGREE OF DIFFERENTIAL EQUATION

    CHHAYA PUBLICATION|Exercise Sample Questions for Competitive Examination (E Assertion - Reasion Type )|2 Videos

Similar Questions

Explore conceptually related problems

Obtain the sum of (1)/(x+1)+(2)/(x^(2)+1)+(4)/(x^(4)+1)+...+ (2^(n))/(x^(2^(n))+1)

(x^(2^n)-y^(2^n))/(x^(2^(n-1))+y^(2^(n-1)))=

(x^(2^(n-1))+y^(2^(n-1)))(x^(2^(n-1))-y^(2^(n-1)))=

If nge2 is an integer, prove by induction that, 1+(1)/(4)+(1)/(9)+ . . .+(1)/(n^(2))lt2-(1)/(n) .

Prove that 1+(1+x)+(1+x+x^(2))+(1+x+x^(2)+x^(3))+...+ to n terms =(n)/(1-x)-(x(1-x^(n)))/(1-x)^(2)

(d^n)/(dx^n)(logx)=? (a) ((n-1)!)/(x^n) (b) (n !)/(x^n) (c) ((n-2)!)/(x^n) (d) (-1)^(n-1)((n-1)!)/(x^n)

Prove that cos^(-1)((1-x^(2n))/(1+x^(2n)))=2tan^(-1)x^n ,0 lt x llt oo

lim_(xto1) ((1-x)(1-x^(2))...(1-x^(2n)))/({(1-x)(1-x^(2))...(1-x^(n))}^(2)), n in N , equals

If y=((1+x)/(1-x))^(n) , prove that (1-x^(2))(d^(2)y)/(dx^(2))=2(n+x)(dy)/(dx).

Prove by mathematical induction that, 1^(2)-2^(2)+3^(2)-4^(2)+ . . .. +(-1)^(n-1)*n^(2)=(-1)^(n-1)*(n(n+1))/(2),ninNN .

CHHAYA PUBLICATION-MISCELLANEOUS EXAMPLES-ALGEBRA
  1. Find the sum of all multiples 3 or 4 between 1 and 325.

    Text Solution

    |

  2. The vertices A,B,C of an isosceles right angled triangle with right an...

    Text Solution

    |

  3. If n ge0 is integer, using induction method prove that, (1)/(1+x)+(2...

    Text Solution

    |

  4. Find the differential coefficient of: x^(5x)

    Text Solution

    |

  5. If x+y=a+b and x^(2)+y^(2)=a^(2)+b^(2), then by mathematical induction...

    Text Solution

    |

  6. By the principle of mathematical induction prove that, (2^(2^(n))+1) h...

    Text Solution

    |

  7. Find the differential coefficient of: x^(9)-5x^(2)+3x

    Text Solution

    |

  8. Find the solution set of inequation (x-2)/(x+5) gt2.

    Text Solution

    |

  9. Find the differential coefficient of: x^(5)+4x

    Text Solution

    |

  10. Find the differential coefficient of: x^(2x)

    Text Solution

    |

  11. Using mathematical induction prove that, "tan"^(-1)(x)/(1*2+x^(2))+"...

    Text Solution

    |

  12. Using mathematical induction prove that, "tan"^(-1)(1)/(3)+"tan"^(-1...

    Text Solution

    |

  13. Using mathematical induction prove that, tan^(-1)((1)/(2*1^(2)))+tan...

    Text Solution

    |

  14. If (1+x+x^(2))^(n)=a(0)+a(1)+x+a(2)x^(2)+...+a(2n)x^(2n), show that a(...

    Text Solution

    |

  15. If (1+x)^(n)=C(0)+C(1)+x+C(2)x^(2)+...+C(n) x^(n) Find the value of ...

    Text Solution

    |

  16. If (1+x)^(n)=C(0)+C(1)+x+C(2)x^(2)+...+C(n) x^(n) Show that C(1)-(1)...

    Text Solution

    |

  17. If (1+x)^(n)=C(0)+C(1)+x+C(2)x^(2)+...+C(n) x^(n) Show that 1^(2)*C...

    Text Solution

    |

  18. If (1+x)^(n)=C(0)+C(1)+x+C(2)x^(2)+...+C(n) x^(n) Show that C(0)^(2)...

    Text Solution

    |

  19. If (1+x)^(n)=C(0)+C(1)+x+C(2)x^(2)+...+C(n) x^(n) Show that (2^(2)*C...

    Text Solution

    |

  20. If (1+x)^(n)=C(0)+C(1)+x+C(2)x^(2)+...+C(n) x^(n) For all values of ...

    Text Solution

    |