Home
Class 14
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

B

x+y+1/xy

C

xy/x-y

D

xy/x+y-1

Text Solution

Verified by Experts

The correct Answer is:
D
Promotional Banner

Topper's Solved these Questions

  • RATIO, PROPORTION & VARIATION

    QUANTUM CAT|Exercise QUESTION BANK|238 Videos

  • SET THEORY

    QUANTUM CAT|Exercise QUESTION BANK|81 Videos

Similar Questions

Explore conceptually related problems

If |x| lt 1 ,then the sum of the series 1 + 2x + 3x^(2) + 4x^(2) + ....infty will be

If (x^(2) + x)/(1-x) = a_(1) x + a_(2) x^(2) + ... to infty , |x| lt 1, then

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

y = sin ^(-1)((1 - x^(2))/(1+ x^(2))) 0 lt x lt 1

QUANTUM CAT-SEQUENCE, SERIES & PROGRESSIONS-QUESTION BANK
  1. In a set of four numbers the first three are in G.P and the llast thre...

    Text Solution

    |

  2. The sum of an infinite G.P. is 16 and the sum of the squares of its te...

    Text Solution

    |

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

    Text Solution

    |

  4. A person is entitled to receive an annual payment which for each ye...

    Text Solution

    |

  5. What is the the sum of the infinite geometric series 1/4 - 3/(16) + 9...

    Text Solution

    |

  6. The sum of first two terms of a G.P. is 5/3 and the sum to infinity of...

    Text Solution

    |

  7. A ball is dropped from a height of 96 feet and it rebounds 2/3 of the ...

    Text Solution

    |

  8. Find the 10th term of the H.P. 1, 1/3 , 1/5 , 1/7 , 1/9 , 1/(11) ,….

    Text Solution

    |

  9. If the 4th and the 7th terms of an H.P. are 1/2 and 2/7 respectively ....

    Text Solution

    |

  10. Find the sum of n terms of the series 1+4/5+7/(5^2)+10+5^3+dot

    Text Solution

    |

  11. Find the sum to n terms of the series 1+4/5+7/5^2+10/5^3+……find the su...

    Text Solution

    |

  12. Which one of the following is true about A.M. , G.M. and H.M. :

    Text Solution

    |

  13. If a,b,c are in A.P. b, c,d are in G.P. and c,d,e are in H.P., then wh...

    Text Solution

    |

  14. If A.M. and G.M. of two numbers is 10 and 8 respectively then find the...

    Text Solution

    |

  15. Find the number of terms in the G.P. whose first term is 3 sum is (409...

    Text Solution

    |

  16. Find the common ratio of the G.P. whose first and last terms are 5 and...

    Text Solution

    |

  17. Find the sum of the series 2sqrt3 , 2sqrt2 , 4/(sqrt3) , ….

    Text Solution

    |

  18. The number of terms in an A.P. is even , the sum of odd terms is 63 a...

    Text Solution

    |

  19. The sum of four consecutive terms in A.P. is 36 and the ratio of produ...

    Text Solution

    |

  20. Find the sum of the three number in G.P. whose product is 216 and the ...

    Text Solution

    |