Home
Class 11
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)`

Text Solution

AI Generated Solution

Promotional Banner

Topper's Solved these Questions

  • RELATIONS AND FUNCTIONS

    CENGAGE ENGLISH|Exercise All Questions|9 Videos
  • STRAIGHT LINES

    CENGAGE ENGLISH|Exercise All Questions|491 Videos

Similar Questions

Explore conceptually related problems

Let T_r denote the rth term of a G.P. for r=1,2,3, If for some positive integers ma n d 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 be the r th term of an A.P. whose first term is a and conmon difference is d . If for some positive integers m ,n, T_(n)= (1)/(m) , T_(m) = (1)/(n) then (a – d) equals

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/na n dT_n=1/m ,t h e nT_(m n) equals a. 1/(m n) b. 1/m+1/n c. 1 d. 0

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

If T_(r) be the rth term of an A.P. with first term a and common difference d, T_(m)=1/n and T_(n)=1/m then a-d equals

If S_n denotes the sum of first n terms of an A.P. such that (S_m)/(S_n)=(m^2)/(n^2),\ t h e n(a_m)/(a_n)= a. (2m+1)/(2n+1) b. (2m-1)/(2n-1) c. (m-1)/(n-1) d. (m+1)/(n+1)

If the m^(t h) term of an A.P. is 1/n and the n^(t h) terms is 1/m , show that the sum of m n terms is 1/2(m n+1)dot

If the ratio of the sum of m terms and n terms of an A.P. be m^2 : n^2 , prove that the ratio of its mth and nth terms is (2m-1): (2n-1) .

The ratio of the sum of m and n terms of an A.P. is m^2: n^2dot Show that the ratio of the mth and nth terms is (2m-1):(2n-1)dot

The ratio of the sum of m and n terms of an A.P. is m^(2) :n^(2) . Show that the ratio mth and nth term is (2m-1) : (2n-1).

CENGAGE ENGLISH-SEQUENCES AND SERIES-All Questions
  1. If (1-p)(1+3x+9x^2+27 x^3+81 x^4+243 x^5)=1-p^6,p!=1 , then the value ...

    Text Solution

    |

  2. ABCD is a square of length a, a in N, a > 1. Let L1, L2 , L3... be poi...

    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. If (1+3+5++p)+(1+3+5++q)=(1+3+5++r) where each set of parentheses cont...

    Text Solution

    |

  5. If a x^3+b x^2+c x+d is divisible by a x^2+c ,t h e na ,b ,c ,d are in...

    Text Solution

    |

  6. The line x+ y = 1 meets X-axis at A and Y-axis at B,P is the mid-poin...

    Text Solution

    |

  7. In a geometric series, the first term is a and common ratio is rdot If...

    Text Solution

    |

  8. If x ,y ,a n dz are distinct prime numbers, then (a).x , y , a n dz ma...

    Text Solution

    |

  9. If x ,y , and z are in G.P. and x+3,y+3, and z+3 are in H.P., then y=2...

    Text Solution

    |

  10. If A.M., G.M., and H.M. of the first and last terms of the series of 1...

    Text Solution

    |

  11. The sum 1+3+7+15+31+...to100 terms is a. 2^(100)-102 b. 2^(99)-101 c...

    Text Solution

    |

  12. In a sequence of (4n + 1) terms the first (2n + 1) terms are in AP wh...

    Text Solution

    |

  13. The coefficient of x^(49) in the product (x-1)(x-3)(x-99)i s a. -99^...

    Text Solution

    |

  14. Let S=4/(19)+(44)/(19^2)+(444)/(19^3)+ u ptooo . Then s is equal to a....

    Text Solution

    |

  15. If Hn=1+1/2+...+1/ndot , then the value of Sn=1+3/2+5/3+...+(99)/(50) ...

    Text Solution

    |

  16. If the sum to infinity of the series 1+2r+3r^2+4r^3+ is 9/4, then val...

    Text Solution

    |

  17. The sum o f series 1+4/5+7/(5^2)+(10)/(5^3)+oo is a. 7//16 b. 5//16 ...

    Text Solution

    |

  18. The sum 20 terms of a series whose rth term is given by Tr=(-1)^r((r^2...

    Text Solution

    |

  19. Consider the sequence 1,2,2,4,4,4,4,8,8,8,8,8,8,8,8,... Then 1025th te...

    Text Solution

    |

  20. If a ,1/b ,c and1/p ,q ,1/r form two arithmetic progressions of the c...

    Text Solution

    |