Home
Class 11
MATHS
Find the sum of n terms of the series 1...

Find the sum of n terms of the series
`1*2*3+2*3*4+3*4*5...........`

Text Solution

Verified by Experts

The given series is `1 xx 2 xx 3+2 xx 3 xx 4+3 xx 4 xx 5+.....`
`n^(th)`term,`a_n=n(n+1)(n+2)`
`=(n^2+n)(n+2)`
`=n^3+3n^2+2n`
...
Promotional Banner

Topper's Solved these Questions

  • SINE AND COSINE FORMULAE AND THEIR APPLICATIONS

    RD SHARMA|Exercise Solved Examples And Exercises|118 Videos
  • STATISTICS

    RD SHARMA|Exercise Solved Examples And Exercises|175 Videos

Similar Questions

Explore conceptually related problems

Find the sum to n terms of the series 1 *2 *3 + 2*4*6 + 3*6*9+...

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

Find the sum to n terms of the series 1xx2+2xx3+3xx4+4xx5+......

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

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

Find the nth term and the sum of n terms of the series 1.2.4+2.3.5+3.4.6+....

Find the sum to n terms of the series: 1xx2xx3+2xx3xx4+3xx4xx5+.

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

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

(2a^(2)-1)/(n),4a-(3)/(a),(6a^(2)-5)/(a)15. Find the sum of n terms of the series,36a- 5

RD SHARMA-SOME SPECIAL SERIES-Solved Examples And Exercises
  1. The sum of the series: 1/((log)2 4)+1/((log)4 4)+1/((log)8 4)++1/((log...

    Text Solution

    |

  2. The sum n terms of the series 1/(sqrt(1)+sqrt(3))+1/(sqrt(3)+sqrt(5))+...

    Text Solution

    |

  3. Find the sum of n terms of the series 1*2*3+2*3*4+3*4*5...........

    Text Solution

    |

  4. Sum the series 3. 8+6. 11+9. 14+ . . . to n terms.

    Text Solution

    |

  5. Find the sum of n terms of the series whose n t h term is: 2n^2-3n+5

    Text Solution

    |

  6. Find the sum to n terms of the series whose nth term is n^2+2^n.

    Text Solution

    |

  7. Find the sum of the series (1^3)/1+(1^3+2^3)/(1+3)+(1^3+2^3+3^3)/(1+3...

    Text Solution

    |

  8. Show that (1xx2^2+2xx3^2+. . . +nxx(n+1)^2)/(1^2xx2+2^2xx3+. . . +n^2x...

    Text Solution

    |

  9. If S1, S2, S3 are the sums of first n natural numbers, their squares a...

    Text Solution

    |

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

    Text Solution

    |

  11. The sequence N of natural numbers is divided into classes as follows. ...

    Text Solution

    |

  12. Find the sum of the following series to n term: 1^3+3^3+5^3+7^3+.........

    Text Solution

    |

  13. Find the sum of the following series to n term: 2^3+4^3+6^3+8^3+.........

    Text Solution

    |

  14. Find the sum of the following series to n term: 1. 2. 5+2. 3. 6+3. 4. ...

    Text Solution

    |

  15. Find the sum of the following series to n term: 1. 2. 4+2. 3. 7+3. 4. ...

    Text Solution

    |

  16. Find the sum to 10 terms of the series 1xx2+2xx3+ 3xx4+ 4xx5+......

    Text Solution

    |

  17. Find the sum of the following series to n term: 3xx1^2+5xx2^2+7xx3^2+....

    Text Solution

    |

  18. Find the sum of the following series whose n t h term is: 2n^3+3n^2-1.

    Text Solution

    |

  19. Find the sum of the following series whose n t h term is: n^3-3^ndot

    Text Solution

    |

  20. Find the sum of the following series whose n th term is: n(n+1)(n+4)

    Text Solution

    |