Home
Class 12
MATHS
If x = 1 + a + a^(2) + …. infty " , ...

If x = 1 + a + `a^(2) + …. infty " , " y = 1 + b + b^(2) + …. infty, " " |a| lt 1 , |b| lt 1, ` then ` 1 + ab + a^(2) b^(2) + ….. infty = `

A

`(xy)/(x + y - 1)`

B

`(x + y - 1)/(xy)`

C

`(xy)/(x + y + 1)`

D

`(x + y + 1)/(xy)`

Text Solution

Verified by Experts

The correct Answer is:
A
Promotional Banner

Topper's Solved these Questions

  • RELATIONS

    DIPTI PUBLICATION ( AP EAMET)|Exercise Exercise|49 Videos

  • SETS ( APPENDIX - 1)

    DIPTI PUBLICATION ( AP EAMET)|Exercise EXERCISE|70 Videos

Similar Questions

Explore conceptually related problems

1 + (0.04) + (0.04)^(2) + …. infty =

If |x| lt 1, then 1/2 log ((1+x)/(1-x)) =

Let f(x) = ab sin x+ b sqrt( 1-a^2) cos x+c , where |a| lt 1, b gt 0 then

If |x| lt 1 , then (1)/(2) log((1+x)/(1-x))=

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

If a lt c lt b , and if 1 -k_(1) lt ln ((b)/(a)) lt k_(2) -1 , then ( k _(1) , k_(2)) is

If a_(1) lt ( 257)^(1//4) -4 lt b _(1) , then (a_(1) , b_(1) ) ( a_(1) , b_(1)) is

If |a| lt 1 and |b| lt 1 , then the sum of the series 1 + (1+a) b + (1 + a + a^(2))b^(2) + (1+ a+ a^(2) + a^(3))b^(3) … is

If a_(1) lt ( 28)^((1)/( 3)) - 3 lt b_(1) , then (a_(1) b_(1)) ( a_(1) , b_(1)) is

If 0 lt y lt 1 , then sum_(n=1)^(oo)(1)/(2n-1)*y^(n+1)=……

DIPTI PUBLICATION ( AP EAMET)-SEQUENCES AND SERIES -EXERCISE
  1. 1 + (0.04) + (0.04)^(2) + …. infty =

    Text Solution

    |

  2. If |x| lt 1, y = x - x^(2) + x^(3) - x^(4) + ….. , the value of x in t...

    Text Solution

    |

  3. If x = 1 + a + a^(2) + …. infty " , " y = 1 + b + b^(2) + …...

    Text Solution

    |

  4. If x = sum(n = 0)^(infty) a^(n) , y = sum(n = 0)^(infty) b^(n) , z = s...

    Text Solution

    |

  5. If exp{ (sin^(2) x + sin^(4) x + sin^(6) x + …. "Upto" infty) log(e) 2...

    Text Solution

    |

  6. If exp { (tan^(2) x -tan^(4) x + tan^(8) x - tan^(6) x …. ) log(e) 16 ...

    Text Solution

    |

  7. For 0 lt x lt pi the values of x which satisfy the relation 9^(1 + ...

    Text Solution

    |

  8. Given that 0 lt x lt (pi)/(4), (pi)/(4) lt y lt (pi)/(2) and sum(k = 0...

    Text Solution

    |

  9. The coefficient of x in (x^2 +(c )/(x))^5 is

    Text Solution

    |

  10. (1)/(2) + (1)/(4) + (1)/(8) + (1)/(16) + ….. = x , (1)/(3) + (1)/(9) +...

    Text Solution

    |

  11. the sum to infinity of (1)/(7) + (2)/(7^(2)) + (1)/(7^(3)) + (2)/(7^(4...

    Text Solution

    |

  12. The sum of an infinite G.P. is 2. If the sum of their squares is 4/3, ...

    Text Solution

    |

  13. The least value of n for which 1 + 2 + 2^(2) + …… to n terms is great...

    Text Solution

    |

  14. If x gt 0, and log(2) + log(2)(sqrt(x)) + log(2) (4sqrt(x)) + log(2) (...

    Text Solution

    |

  15. If (1 + 3 + 5 + …. +P ) + (1 + 3 + 5 + …. Q) = (1 + 3 + 5 + … r) where...

    Text Solution

    |

  16. The greatest value on n so that 1 + 5 +5^(2) + 5^(3) + …. N terms is ...

    Text Solution

    |

  17. 7 + 77 + 777 + …. N terms =

    Text Solution

    |

  18. 6 + 66 + 666 + ….n terms =

    Text Solution

    |

  19. The sum to n terms of the series .5 + .55 + .555 + ….. Is

    Text Solution

    |

  20. 7 + 77 + 777 + …. N terms =

    Text Solution

    |