Home
Class 12
MATHS
Find the sum to n terms of the series: 3...

Find the sum to `n` terms of the series: `3/(1^^2 .2^2)+5/(2^2 .3^2)+7/(3^2 .4^2)+`

Text Solution

Verified by Experts

The correct Answer is:
`(2n + n ^(2))/( (n +1 ) ^(2))`
Promotional Banner

Topper's Solved these Questions

  • SEQUENCE & SERIES

    RESONANCE|Exercise EXERCISE -1 PART -I RMO|44 Videos

  • SEQUENCE & SERIES

    RESONANCE|Exercise EXERCISE -1 PART -II RMO|3 Videos

  • SEQUENCE & SERIES

    RESONANCE|Exercise EXERCISE -2 (PART-II : PREVIOUSLY ASKED QUESTION OF RMO)|3 Videos

  • RELATION, FUNCTION & ITF

    RESONANCE|Exercise SSP|55 Videos

  • TEST PAPER

    RESONANCE|Exercise CHEMISTRY|37 Videos

Similar Questions

Explore conceptually related problems

Find the sum of first n terms of the series 3/(1^(2).2^(2))+5/(2^(2).3^(2))+7/(3^(2).4^(2))+.......+ and deduce the sum of infinity .

Find the sum to n terms of the series 3/(1^(2)xx2^(2))+5/(2^(2)xx3^(2))+7/(3^(2)xx4^(2))+

Find the sum to n terms of the series 1.2.3+2.3.4+3.4.5+…

Find the sum of n terms of the series 1.2^(2)+2.3^(2)+3.4^(2)+

Find the sum to n terms of the series 1*2^(2)+2*3^(2)+3*4^(2)+...

The sum to n term of the series 1(1!)+2(2!)+3(3!)+

The sum to n term of the series 1(1!)+2(2!)+3(3!)+

Find the sum to n terms of the series: 1+2x+3x^(2)+4x^(3)+......

RESONANCE-SEQUENCE & SERIES -SELF PRACTICE PROBLEMS
  1. Find the maximum sum of the A.P. 40 +38+36+34+32+……………

    Text Solution

    |

  2. Find the sum of first 16 terms of an A.P. a (1), a (2), a(3)……….. If...

    Text Solution

    |

  3. There are n A.M.'s between 3 and 29 such that 6th mean : (n - 1)th mea...

    Text Solution

    |

  4. For what value of n , (a ^(n +3) + b ^(n +3))/(a ^(n +2) + b ^(n +2)),...

    Text Solution

    |

  5. Find the G.P. if the common ratio of G.P. is 3, n^(th) term is 486 an...

    Text Solution

    |

  6. if x , 2y and 3z are in AP where the distinct numbers x, yand z ar...

    Text Solution

    |

  7. A G.P consists of 2n terms . If the sum of the terms . If the sum of ...

    Text Solution

    |

  8. If the continued product of three numbers in G.P. is 216 and the sum o...

    Text Solution

    |

  9. Find the value of n so that (a ^(n +2) + b ^(n +1))/( a ^(n) + b ^(n))...

    Text Solution

    |

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

    Text Solution

    |

  11. If the harmonic mean between two positive numbers is to their G.M. as ...

    Text Solution

    |

  12. a,b,c are in H.P. then prove that (b +a)/(b-a) + (b+c)/(b-c) =2

    Text Solution

    |

  13. If a,b,c,d are in H.P., then ab+bc+cd is equal to

    Text Solution

    |

  14. If 4 + (4 +d)/( 5) + (4 + 2d)/(5 ^(2)) ……….=1, then find d.

    Text Solution

    |

  15. Evaluate :1 + 3x + 6x ^(2) + 10 x ^(3)+……. upto infinite term, whre |x...

    Text Solution

    |

  16. Sum of the series :1 + 2 (1 + (1)/(n)) + 3 (1 + (1)/(n )) ^(2) + ………

    Text Solution

    |

  17. Find the sum to n terms of the series: 3/(1^^2 .2^2)+5/(2^2 .3^2)+7/(3...

    Text Solution

    |

  18. Find the sum to n terms of the series 1+ (1+2) + (1+2+3) + (1+2+ 3+...

    Text Solution

    |

  19. Generate term of the series 4 + 14 + 30 + 52+ 82+ 114+.........

    Text Solution

    |

  20. If sum (r =1) ^(n ) T (r) = (n +1) ( n +2) ( n +3) then find sum ( r ...

    Text Solution

    |