Home
Class 12
MATHS
If x=sum(n=0)^oo a^n, y=sum(n=0)^oo b^n ...

If `x=sum_(n=0)^oo a^n, y=sum_(n=0)^oo b^n` where `|a|<1,|b|<1` then prove that `sum_(n=0)^oo (ab)^n=(xy)/(x+y-1)`

Promotional Banner

Topper's Solved these Questions

  • Product of two Vectors

    A DAS GUPTA|Exercise Exercise|48 Videos

  • Properties and Application of definite Integrals

    A DAS GUPTA|Exercise EXERCISE|62 Videos

Similar Questions

Explore conceptually related problems

If x=sum_(n=0)^oo a^n, y=sum_(n=0)^oo b^n, z=sum_(n=0)^oo c^n where a,b,c are in A.P and |a|<1, |b<1, |c|<1, then x,y,z are in

If x = sum_(n=0)^(oo) a^(n), y=sum_(n=0)^(oo) b^(n), z = sum_(n=0)^(oo) C^(n) where a,b,c are in A.P. and |a| lt 1, |b| lt 1, |c| lt 1 , then x,y,z are in

If a=sum_(n=0)^(oo)x^(n),b=sum_(n=0)^(oo)y^(n),c=sum_(n=0)^(oo)(xy)^(n) where |x|,|y|<1 then

If a=sum_(n=0)^(oo)x^(n),b=sum_(n=0)^(oo)y^(n),c=sum_(n=0)^(oo)(xy)^(n) where |x|,|y|<1 then

If x=sum_(n=0)^(oo) a^(n),y=sum_(n=0)^(oo)b^(n),z=sum_(n=0)^(oo)(ab)^(n) , where a,blt1 , then

If quad sum_(n=0)^(oo)a^(n),y=sum_(n=0)^(oo)b^(n),z=sum_(n=0)^(oo)c^(n), wherer a,b, and c are in A.P.and |a|<,|b|<1, and |c|<1, then prove that x,y and z are in H.P.

If x= sum_(n=0)^oo (Costheta)^(2n) , y= sum_(n=0)^oo (Sinphi)^(2n) , z= sum_(n=0)^oo (Cosphi)^(2n). (Sintheta)^(2n) Then which of the following is true ??

If a,b,c are proper fractiion are in H.P. and x sum_(n=1)^oo a^n, y=sum_(n=1)^oo b^n, z= sum_(n=1)^oo c^n then x,y,z are in (A) A.P. (B) G.P. (C) H.P. (D) none of these

If x=Sigma_(n=0)^(oo) a^n,y=Sigma_(n=0)^(oo) b^n,z=Sigma_(n=0)^(oo) c^n where a, b,and c are in A.P and |a|lt 1 ,|b|lt 1 and |c|1 then prove that x,y and z are in H.P

A DAS GUPTA-Progression, Related Inequalities and Series-Exercise
  1. If the sum of an infinite G.P is 32 and the some of its first two term...

    Text Solution

    |

  2. If Sn=1+r^n+r^(2n)+r^(3n)+.... to oo and sn=1-r^n+r^(2n)-r^(3n)+... to...

    Text Solution

    |

  3. If x=sum(n=0)^oo a^n, y=sum(n=0)^oo b^n where |a|<1,|b|<1 then prove t...

    Text Solution

    |

  4. If exp. {(sin^2x+sin^4x+sin^6x+…inf.) In2} satisfies the equation x^2-...

    Text Solution

    |

  5. If S1, S2,S3,S4,.....,Sp denotes the sums of infinite geometric serie...

    Text Solution

    |

  6. If S1, S2,S3,S4,.....,Sp denotes the sums of infinite geometric serie...

    Text Solution

    |

  7. If S1, S2,S3,S4,.....,Sp denotes the sums of infinite geometric serie...

    Text Solution

    |

  8. If a,b,c are in G.P., then show that : loga, logb, log c are in A.P.

    Text Solution

    |

  9. If a,b,c are in A.P. and x,y,z in G.P., prove that x^(b-c).y^(c-a).z^(...

    Text Solution

    |

  10. If a, b, c are in A.P and a, b, d are in G.P, prove that a, a -b, d ...

    Text Solution

    |

  11. 29. If a,b,c are in G.P. and a^(1/x)=b^(1/y)=c^(1/z) prove that x, y, ...

    Text Solution

    |

  12. If a, x, b as well as c, x, d are in GP while a^2,y,b^2 as well as c^2...

    Text Solution

    |

  13. If pth, qth and rth terms of an A.P. and G.JP. Both be a,b and c respe...

    Text Solution

    |

  14. If pth, qth , rth and sth terms of an AP are in GP then show that (p-q...

    Text Solution

    |

  15. If second third and sixth terms of an A.P. are consecutive terms o a ...

    Text Solution

    |

  16. Find an AP of distinct terms whose first term is unity such that the s...

    Text Solution

    |

  17. In a set of four number, the first three are in GP & the last three ar...

    Text Solution

    |

  18. In a set of four numbers, the first three are in GP and the last three...

    Text Solution

    |

  19. Prove that three unequal numbers cannot be in GP when each number incr...

    Text Solution

    |

  20. Three numbers whose sum is 15 are in A.P. If 1,4,19 be added to them r...

    Text Solution

    |