Home
Class 12
MATHS
If 1+ 2x + 3x^(2) + 4x^(3) + …oo= (9)/(4...

If `1+ 2x + 3x^(2) + 4x^(3) + …oo= (9)/(4) (|x| lt 1)` then x=

A

`1//3`

B

`1//4`

C

`1//5`

D

`1//6`

Text Solution

Verified by Experts

The correct Answer is:
A
Promotional Banner

Topper's Solved these Questions

  • SEQUENCE AND SERIES

    AAKASH SERIES|Exercise Practice Exercise|71 Videos

  • REVISION EXERCISE

    AAKASH SERIES|Exercise STRAIGHT LINES|24 Videos

  • SETS AND RELATIONS

    AAKASH SERIES|Exercise PRACTICE EXERCISE|26 Videos

Similar Questions

Explore conceptually related problems

If f (x) = x-x ^(2) + x ^(3) - x ^(4) +….oo, |x| lt 1, then f '(x)=

If the sum of 1 + 4x + 7x^(2) + 10x^(3) + ….oo (|x|lt 1) is (35)/(16) then x=

If f(x)=x-x^(2)+x^(3)-x^(4)+….oo when |x| lt 1 then f^(-1)(x)=

Assertion (A) : If x+(x^(2))/(2)+(x^(3))/(3)+………oo=log((7)/(6)) then x=(1)/(7) Reason (R ) : If |x| lt 1 , then x+(x^(2))/(2)+(x^(3))/(3)+…..oo=log((1)/(1-x))

If x = 1 + 3a + 6a^2 + 10 a^3 + ……" to " oo terms |a| lt 1, y = 1+4a+10a^2 + 20a^3 + ….." to " oo terms, |a| lt 1 , then x:y

AAKASH SERIES-SEQUENCE AND SERIES-Practice Exercise
  1. If the sum of the series 1+ (3)/(x) + (9)/(x^(2))+ (27)/(x^(3)) + …oo ...

    Text Solution

    |

  2. If 3 + (3 + d) (1)/(4) + (3+ 2d) (1)/(4^(2)) + …oo= 8 then d=

    Text Solution

    |

  3. If 1+ 2x + 3x^(2) + 4x^(3) + …oo= (9)/(4) (|x| lt 1) then x=

    Text Solution

    |

  4. If the sum to infinity of the series 3 + 5x + 7x^(2) + …oo = (44)/(9) ...

    Text Solution

    |

  5. Let p= 3^(1//3) .3^(2//9).3^(3//27) ….oo then p^(1//3)=

    Text Solution

    |

  6. If (a + b e^(x))/(a-b e^(x)) = (b + c e^(x))/(b- c e^(x))= (c + d e^(x...

    Text Solution

    |

  7. Given sum of the first n terms of an A.P is 2n+ 3n^(2). Another A.P is...

    Text Solution

    |

  8. The sum (3)/(1^(2)) + (5)/(1^(2) + 2^(2)) + (7)/(1^(2)+ 2^(2) + 3^(2))...

    Text Solution

    |

  9. Given a sequence of 4 numbers, first three of which are in G.P.,and th...

    Text Solution

    |

  10. The value of 1^(2) + 3^(2) + 5^(2) + …+ 25^(2) is

    Text Solution

    |

  11. Let a(1), a(2), a(3)….. be terms of an A.P. If (a(1) + a(2) + …..a(p))...

    Text Solution

    |

  12. The sum of the series 2^(2) + 2(4^(2)) + 3(6^(2)) + ….upto 10 terms is

    Text Solution

    |

  13. If S= tan^(-1) ((1)/(n^(2) +n+1)) + tan^(-1) ((1)/(n^(2) + 2n+ 3))+ …....

    Text Solution

    |

  14. If a(1), a(2), a(3),…, a(n) are in A.P such that a(4) - a(7) + a(10)= ...

    Text Solution

    |

  15. Given an A.P whose terms are all positive integers. The sum of its nin...

    Text Solution

    |

  16. If the sum (3)/(1^(2)) + (5)/(1^(2) + 2^(2)) + (7)/(1^(2) + 2^(2) + 3^...

    Text Solution

    |

  17. In a geometric progression, if the ratio of the sum of first 5 terms t...

    Text Solution

    |

  18. The sum of the first 20 terms common between the series 3+7 + 11 + 15…...

    Text Solution

    |

  19. Let G be the geometric mean of two positive numbers a and b, and M be ...

    Text Solution

    |

  20. The lest positive integer n such that 1- (2)/(3)- (2)/(3^(2))- ….- (2)...

    Text Solution

    |