Home
Class 12
MATHS
The sum of first 'n' terms of the series...

The sum of first 'n' terms of the series `1^2+(1)(2)+3^2+(3)(4)+5^2+(5)(6)+7^2+.......` when n is odd is

A

`(1)/(12)(n+1)(4n^(2)-n+3)`

B

`(1)/(12)n(4n^(2)+3n-4)`

C

`(1)/(6)(n+1)(4n^(2)-n+5)`

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
A
Promotional Banner

Topper's Solved these Questions

  • PROGRESSIONS

    MCGROW HILL PUBLICATION|Exercise EXERCISES LEVEL-2 (Single Correct Answer Type Questions)|11 Videos

  • PROGRESSIONS

    MCGROW HILL PUBLICATION|Exercise EXERCISES (Numerical Answer Type Questions)|19 Videos

  • PROGRESSIONS

    MCGROW HILL PUBLICATION|Exercise EXERCISES CONCEPT-BASED (Single Correct Answer Type Questions)|15 Videos

  • PROBABILITY

    MCGROW HILL PUBLICATION|Exercise Previous Years B-Architecture Entrance Examination Papers|21 Videos

  • QUADRATIC EQUATIONS

    MCGROW HILL PUBLICATION|Exercise Questions from previous Years. B - architecture entrance examination papers|16 Videos

Similar Questions

Explore conceptually related problems

The sum of first backslash n' terms of the series 1^(2)+(1)(2)+3^(2)+(3)(4)+5^(2)+(5)(6)+7^(2)+ when n is odd is

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!)+

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

The sum of the first n terms of the series 1^(2)+2.2^(2)+3^(2)+2.4^(2)+5^(2)+2.6^(2)+... is

The sum of the first n terms of the series (1)/(2)+(3)/(4)+(7)/(8)+(15)/(16)+.... is equal to

Find the sum of n terms of the series 1^3+3.2^2+3^3+3.4^2+5^3+3.6^2+....... when (i)n is odd (ii)n is even

MCGROW HILL PUBLICATION-PROGRESSIONS-EXERCISES LEVEL-1 (Single Correct Answer Type Questions)
  1. If n!, 3n! and (n-1)! are in G.P then n!, 5n! and (n+1)! are in

    Text Solution

    |

  2. If S(n)=81+54+36+24+.. upto n terms, then value of x=(S(n)-4S(n-1)+6S(...

    Text Solution

    |

  3. The sum of first 'n' terms of the series 1^2+(1)(2)+3^2+(3)(4)+5^2+(5)...

    Text Solution

    |

  4. If L = underset( n rarr oo)lim (1+3^(-1))(1+3^(-2))+(1+3^(-4))+(1+3^(-...

    Text Solution

    |

  5. If a1,a2,a3,.......an, are 'n', distinct odd natural numbers, not divi...

    Text Solution

    |

  6. Coefficient of x^(99) in the expansion of (x-1) (x-3)(x-5)..(x-1999) i...

    Text Solution

    |

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

    Text Solution

    |

  8. If x= overset(oo)underset(n =0)Sigma a^(n),y= overset(oo)underset(n=0)...

    Text Solution

    |

  9. If the sum of an infinite decreasing G.P. is 3 and sum of the cubes of...

    Text Solution

    |

  10. The sum of the series S= overset(n)underset(r=1)Sigma log ((a^(r+1))/(...

    Text Solution

    |

  11. If the fifth term of a G.P. is 2, then write the product of its 9 t...

    Text Solution

    |

  12. If s is the sum to infnity of a G.P, whose first term is a, then the s...

    Text Solution

    |

  13. For a sequence lt a(n) gt, a(1) =5 and (a(r+1))/(a(r))=(1)/(2) AA r, t...

    Text Solution

    |

  14. If the H.M.of two numbers is to their GM. is 12:13 then the numbers ar...

    Text Solution

    |

  15. The H.M. between two numbers is 16/5, their A.M. is A and G.M. is G. I...

    Text Solution

    |

  16. If a(r)=a+(r-1)d is rth term of an A.P., then a(n)^(2)-2a(n-1)^(2)+a(n...

    Text Solution

    |

  17. If A=1+r^2+r^(2a)+...oo=a and B=1+r^b+r^(2b)+...oo=b then a/b is equal...

    Text Solution

    |

  18. Suppose a(1)=45, a(2)=41 and a(k)=2a(k-1)-a(k-2) AA k ge 3, then, valu...

    Text Solution

    |

  19. Suppose P(x)=1-x+x^(2)-x^(3)+…+x^(2012) is expressed as a polynomial i...

    Text Solution

    |

  20. The sum of first 26 terms of an A.P. a(1),a(2),a(3),.. if a(2)+a(6)+a(...

    Text Solution

    |