Home
Class 12
MATHS
Find the sum of the following series : ...

Find the sum of the following series :
`3.1^(2) + 4.2^(2) + 5.3^(2) +…+(n+2). n^(2)`

Text Solution

Verified by Experts

The correct Answer is:
`(1)/(12)n(n+1)(3n^(2) + 11n + 4)`
Promotional Banner

Topper's Solved these Questions

  • SEQUENCE AND SERIES

    CHHAYA PUBLICATION|Exercise Exercise 9 C (Multiple Choice Type Questions)|14 Videos

  • SEQUENCE AND SERIES

    CHHAYA PUBLICATION|Exercise Exercise 9 C (Very Short Answer Type Questions)|17 Videos

  • SEQUENCE AND SERIES

    CHHAYA PUBLICATION|Exercise Exercise 9 B (Short Answer Type Questions)|42 Videos

  • SECOND ORDER DERIVATIVE

    CHHAYA PUBLICATION|Exercise Sample Question for Competitive Examination (Assertion-Reason type)|2 Videos

  • SET THEORY

    CHHAYA PUBLICATION|Exercise Assertion-Reason Type|2 Videos

Similar Questions

Explore conceptually related problems

Find the sum to n terms of each of the following series : 1^(2) - 2^(2)+3^(2) - 4^(2) + 5^(2) - 6^(2)+…

Find the sum of first n terms of the following series : 1.2^(2) + 2.3^(2) + 3.4^(2)+…

Find the sum to n terms of each of the following series : 1^(2) + 3^(2) + 5^(2) +…

Find the sum to n terms of the following series : 1+2a + 3 a^(2) + 4a^(3) + …, [a != 1]

Find the sum to n terms of the following series : (1) + (1+3) + (1+3+3^(2)) +…

Find the sum to n terms of each of the following series : (1^(2)) + (1^(2)+2^(2)) + (1^(2) + 2^(2) + 3^(2)) +…

Find the sum to n terms of each of the following series : (3^(3) - 2^(3)) + (5^(3) - 4^(3)) + (7^(3) - 6^(3))+…

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

Find the sum to n terms of each of the following series : n.1 + (n-1).2+(n-2). 3+(n-3).4+…

Find the sum of the following series (1)+(2+3)+(4+5+6)+(7+8+9+10)+…to n terms.

CHHAYA PUBLICATION-SEQUENCE AND SERIES-Exercise 9 B (Long Answer Type Questions)
  1. Find the sum to n terms of each of the following series : 1^(2) + 3^...

    Text Solution

    |

  2. Find the sum to n terms of each of the following series : 1.3 .5 + 3...

    Text Solution

    |

  3. Find the sum of the following series : 3.1^(2) + 4.2^(2) + 5.3^(2) +...

    Text Solution

    |

  4. Find the sum of the following series : 1+3+6+10+15+… to n terms.

    Text Solution

    |

  5. Find the sum of the following series : 1+5+12+22+35+…. to n terms.

    Text Solution

    |

  6. The sum of first n terms of a series is n^(2) + an + b. Show that b = ...

    Text Solution

    |

  7. If n is a positive integer, show that, (n+1)^(2) + (n+2)^(2) + …+ 4n...

    Text Solution

    |

  8. Find the sum to n terms of each of the following series : (1) + (1+2...

    Text Solution

    |

  9. Find the sum to n terms of each of the following series : (1^(2)) + ...

    Text Solution

    |

  10. Find the sum to n terms of each of the following series : (3^(3) - 2...

    Text Solution

    |

  11. Find the sum to n terms of each of the following series : (1) + (2+3...

    Text Solution

    |

  12. Find the sum to n terms of each of the following series : (1)/(1.4) ...

    Text Solution

    |

  13. Find the sum to n terms of each of the following series : (1)/(2.5) ...

    Text Solution

    |

  14. Find the sum to n terms of each of the following series : n.1 + (n-1...

    Text Solution

    |

  15. The sum of first P terms of an A.P. is equal to the sum of its first Q...

    Text Solution

    |

  16. A series is given in the form : (1) + (2+3+4) + (5+6+7+8+9) +…. Find t...

    Text Solution

    |

  17. The first and last terms of an A.P. are a and l respectively. If S be ...

    Text Solution

    |

  18. If the first, second and last terms of A.P. be a, b, and c respectivel...

    Text Solution

    |

  19. If S(n) be the sum of n consecutive terms of an A.P. show that, S(n+...

    Text Solution

    |

  20. If S(n) be the sum of n consecutive terms of an A.P. show that, S(n+...

    Text Solution

    |