Home
Class 11
MATHS
If sum of x terms of a series is S(x)=(1...

If sum of x terms of a series is `S_(x)=(1)/((2x+3)(2x+1))`
whose `r^(th)` term is `T_(r)`. Then, `sum_(r=1)^(n) (1)/(T_(r))` is equal to

A

`(1)/(4)sum(2r+1)(2r-1)(2r+3)`

B

`-(1)/(4)sum(2r+1)(2r-1)(2r+3)`

C

`sum(2r+1)(2r-1)(2r+3)`

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
B
we have, `S_(x)=(1)/((2x+3)(2x+1))`
`:." "T_(x)=S_(x)-S_(x-1)`
`rArr" "T_(x)=(1)/((2x+3)(2x+1))-(1)/((2x+1)(2x-1))`
`rArr" "(-4)/((2x-1)(2x+1)(2x+3))`
`:." "underset(r=1)overset(n)sum(1)/(T_(r))=-(1)/(4)underset(r=1)overset(n)sum(2r-1)(2r+1)(2r+3)`
Promotional Banner

Topper's Solved these Questions

  • SEQUENCES AND SERIES

    OBJECTIVE RD SHARMA|Exercise Section II - Assertion Reason Type|13 Videos

  • SEQUENCES AND SERIES

    OBJECTIVE RD SHARMA|Exercise Exercise|129 Videos

  • SEQUENCES AND SERIES

    OBJECTIVE RD SHARMA|Exercise Chapter Test|60 Videos

  • QUADRATIC EXPRESSIONS AND EQUATIONS

    OBJECTIVE RD SHARMA|Exercise Chapter Test|50 Videos

  • SETS

    OBJECTIVE RD SHARMA|Exercise Chapter Test|30 Videos

Similar Questions

Explore conceptually related problems

If sum of n terms of a sequence is given by S_(n)=3n^(2)-5n+7&t_(r) represents its r^(th) term then

If sum_(r=1)^(n)cos^(-1)x_(r)=0, then sum_(r=1)^(n)x_(r) equals to

lim_(xrarr2)(sum_(r=1)^(n)x^r-sum_(r=1)^(n)2r)/(x-2) is equal to

If x_(1),x_(2),x_(3),......x2_(n) are in A.P, then sum_(r=1)^(2n)(-1)^(r+1)x_(r)^(2) is equal to

Let rth term of a series be given by T_(r)=(r)/(1-3r^(2)+r^(4)) then Lt_(n rarr oo)sum_(r=1)^(n)T_(r)=

The rth term of a series is given by t_(r)=(r)/(1+r^(2)+r_(n)^(4)), then lim(n rarr oo)sum_(r=1)^(n)(t_(r))

OBJECTIVE RD SHARMA-SEQUENCES AND SERIES-Section I - Solved Mcqs
  1. In a sequence of (4n+1) terms, the first (2n+1) terms are n A.P. whose...

    Text Solution

    |

  2. If 3 arithmetic means, 3 geometric means and 3 harmonic means are inse...

    Text Solution

    |

  3. If sum of x terms of a series is S(x)=(1)/((2x+3)(2x+1)) whose r^(th...

    Text Solution

    |

  4. If f(n)=sum(r=1)^(n) r^(4), then the value of sum(r=1)^(n) r(n-r)^(3) ...

    Text Solution

    |

  5. Number of G.P's having 5,9 and 11 as its three terms is equal to

    Text Solution

    |

  6. The largest term common to the sequences 1, 11 , 21 , 31 , to100 term...

    Text Solution

    |

  7. If S(k) denotes the sum of first k terms of a G.P. Then, S(n),S(2n)-S(...

    Text Solution

    |

  8. Four different integers form an increasing A.P One of these numbers is...

    Text Solution

    |

  9. Let there be a GP whose first term is a and the common ratio is r. If ...

    Text Solution

    |

  10. - If log(5c/a),log((3b)/(5c))and log(a/(3b))are in AP, where a, b, c a...

    Text Solution

    |

  11. If a,x,b are in A.P.,a,y,b are in G.P. and a,z,b are in H.P. such that...

    Text Solution

    |

  12. In the sequence 1, 2, 2, 3, 3, 3, 4, 4,4,4,....., where n consecutive ...

    Text Solution

    |

  13. If the sequence 1, 2, 2, 4, 4, 4, 4, 8, 8, 8, 8, 8, 8, 8, 8, ...where ...

    Text Solution

    |

  14. sum(r=1)^(n) r^(2)-sum(r=1)^(n) sum(r=1)^(n) is equal to

    Text Solution

    |

  15. The sum of the products of 2n numbers pm1,pm2,pm3, . . . . ,n taking t...

    Text Solution

    |

  16. If n is an odd integer greater than or equal to 1, then the value of n...

    Text Solution

    |

  17. If sum(k=1)^(n) (sum(m=1)^(k) m^(2))=an^(4)+bn^(3)+cn^(2)+dn+e, then

    Text Solution

    |

  18. If a ,b ,c are three distinct real numbers in G.P. and a+b+c=x b , the...

    Text Solution

    |

  19. Let a1 = 0 and a1, a2,a3,...,an be real numbers such that |ai| = |a(i-...

    Text Solution

    |

  20. If a(1),a(2),a(3), . . .,a(n) are non-zero real numbers such that (a...

    Text Solution

    |