Home
Class 11
MATHS
The sequence N of natural numbers is div...

The sequence N of natural numbers is divided into classes as follows. Show that the sum of the numbers in nth row is `(2n^2+1)`

Text Solution

Verified by Experts

The number of numbers in successive row are `2,4,6` and hence there will be `2n` numbers in `nth` row which will be in the AP of cd `1`. The first term in successive row are
`S=1+3+7+11+....+t_n`
`S=13+7+11+...+t_(n-1)=t_n`
Sutracting `O=1+[2+4+6+(n-1)]`terms`-t_n`
...
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

The sequence of odd natural numbers is divided into groups 1,3,5,7,9,11,"…." and so on. Show that the sum of the numbers in nth group is n^(3) .

84. The natu The natural numbers are written as follows 2 3 7 8 9 10 th The sum of the numbers in the n" row is (A) (n2-1)

Sum of square of n natural number

Natural numbers are divided into groups in the following way: 1,(2,3),(4,5,6),(7,8,9,10), Show that the sum of the numbers in the nth group is (n(n^2+1))/2

RD SHARMA-SOME SPECIAL SERIES-Solved Examples And Exercises
  1. If S1, S2, S3 are the sums of first n natural numbers, their squares a...

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

  13. Find the sum of the following series whose n th term is: (2n-1)^2

    Text Solution

    |

  14. Find the 20th term and the sum of 20 terms of the series: 2xx4+4xx6+6x...

    Text Solution

    |

  15. Find the sum of the first n terms of the series : 3 + 7 + 13 +21 + 31...

    Text Solution

    |

  16. Find the sum of first n terms of the following series:5+11+19+29+41+.....

    Text Solution

    |

  17. Find the sum of n terms\ of the series: 1/(1. 2)+1/(2. 3)+1/(3. 4)+.....

    Text Solution

    |

  18. Sum of the following series to n term: 3+5+9+15\ +23+........

    Text Solution

    |

  19. Sum of the following series to n term: 1+3+7+13+21+ ............

    Text Solution

    |

  20. Sum of the following series to n term: \ 1+3+6+10+15+.............

    Text Solution

    |