Home
Class 12
MATHS
Let Tr a n dSr be the rth term and sum u...

Let `T_r a n dS_r` be the rth term and sum up to rth term of a series, respectively. If for an odd number `n ,S_n=na n dT_n=(T_n-1)/(n^2),t h e nT_m` (`m` being even)is `2/(1+m^2)` b. `(2m^2)/(1+m^2)` c. `((m+1)^2)/(2+(m+1)^2)` d. `(2(m+1)^2)/(1+(m+1)^2)`

A

`2/(1+m^(2))`

B

`(2m^(2))/(1+m^(2))`

C

`((m+1)^(2))/(2+(m+1)^(2))`

D

`(2(m+1)^(2))/(1+(m+1)^(2))`

Text Solution

Verified by Experts

The correct Answer is:
D
Promotional Banner

Topper's Solved these Questions

  • PROGRESSION & SERIES

    FIITJEE|Exercise ASSIGNMENT PROBLEMS (OBJECTIVE) LEVEL-II|20 Videos

  • PROGRESSION & SERIES

    FIITJEE|Exercise COMPREHENSIONS -I|3 Videos

  • PROGRESSION & SERIES

    FIITJEE|Exercise ASSIGNMENT PROBLEMS (SUBJECTIVE) LEVEL-II|17 Videos

  • PROBABILITY

    FIITJEE|Exercise Exercise 7|2 Videos

  • QUADRATIC EQUATION & EXPRESSION

    FIITJEE|Exercise NUMERICAL BASED|3 Videos

Similar Questions

Explore conceptually related problems

Let T_(r) and S_(r) be the rth term and sum up to rth term of a series,respectively.If for an odd number n,S_(n)=n and T_(n)=(T_(n)-1)/(n^(2)), then T_(m)(m being even) is (2)/(1+m^(2)) b.(2m^(2))/(1+m^(2)) c.((m+1)^(2))/(2+(m+1)^(2))d(2(m+1)^(2))/(1+(m+1)^(2))

Let T_(r) be the r^(th) term of an A.P whose first term is a and common difference is d IF for some integer m,n,T_(m)=(1)/(n) and T_(n)=(1)/(m) then a-d=

Let T_(r) be the rth term of an AP, for r=1,2,… If for some positive integers m and n, we have T_(m)=(1)/(n) and T_(n)=(1)/(m)," the "T_(m+n) equals

Let T_(r) denote the rth term of a G.P.for r=1,2,3,... If for some positive integers m and n, we have T_(m)=1/n^(2) and T_(n)=1/m^(2) ,then find the value of T_(m+n/2)

Let T_(r) be the rth term of an A.P.for r=1,2,3,...... If for some positive integers m,n, we have T_(m)=(1)/(n)andT_(n)=(1)/(m), then T_(mn) equals a.(1)/(mn) b.(1)/(m)+(1)/(n) c.1 d.0

FIITJEE-PROGRESSION & SERIES -ASSIGNMENT PROBLEMS (OBJECTIVE) LEVEL-I
  1. The largest interval for which the series 1+(x-1)+(x-1)^(2)+….oo may ...

    Text Solution

    |

  2. If 1/(1^2)+1/(2^2)+1/(3^2)+ tooo=(pi^2)/6,t h e n1/(1^2)+1/(3^2)+1/(5^...

    Text Solution

    |

  3. Let Tr a n dSr be the rth term and sum up to rth term of a series, res...

    Text Solution

    |

  4. Let a1,a2,a3... be in A.P. and ap,aq,ar be in G.P. then value of aq/ap...

    Text Solution

    |

  5. If H(1),H(2),H(3),…..H(2n+1) are in H.P then sum(i=1)^(2n)(-1)^(j)((H(...

    Text Solution

    |

  6. If the sequences 1,2,2,4,4,4,4,8,8,8,8,8,8,8,8….. where n consecutive ...

    Text Solution

    |

  7. If S(r)= sum(r=1)^(n)T(1)=n(n+1)(n+2)(n+3) then sum(r=1)^(10) 1/(T(r))...

    Text Solution

    |

  8. a,b,c,d,e are five numbers in which the first three are in A.P and th...

    Text Solution

    |

  9. The coefficient of x^15 in the product (1-x)(1-2x) (L-2^2 x) (L-2^3 ...

    Text Solution

    |

  10. Sum of n terms of the series (2n-1)+2(2n-3)+3(2n-5)+... is

    Text Solution

    |

  11. The sum of n terms of the series 5/(1.2). 1/3 +7/(2.3). 1/(3^(2))+9/(...

    Text Solution

    |

  12. Let tr=2^(r/2)+2^(-r/2) then sum(r=1)^10 tr^2=

    Text Solution

    |

  13. In a sequence of (4n+1) terms, the first (2n+1) terms are n A.P. whose...

    Text Solution

    |

  14. Let a(1),a(2),a(3),a(4),a(5) be a five term geometric sequence satisfi...

    Text Solution

    |

  15. The nth term of the series 10,23,60,169,494 , …….. is

    Text Solution

    |

  16. The value of sum(n=0)^(m) log ((a^(2n-1))/(b^(m-1)))(a != 0 , 1 , b ...

    Text Solution

    |

  17. A , r = 1 , 2, 3 ….., n are n points on the parabola y^(2)=4x in the...

    Text Solution

    |

  18. Sum to n terms of the series 1^(3) - (1.5)^(3) +2^(3)-(2.5)^(3) +…. is

    Text Solution

    |

  19. Find the sum of the product of every pair of the first n of natural n...

    Text Solution

    |

  20. in the given square, a diagonal is drawn, and parallel line segments j...

    Text Solution

    |