Home
Class 12
MATHS
The sum of first n terms of the series 1...

The sum of first n terms of the series `1^(2)+ 2 . 2^(2) + 3^(2) + 2. 4 ^(2) + 5^(2) +…` is `n/2 (n+1) ^(2)` when n is even , When n is odd then the sum will be-

A

`1/2 n ^(2) (n+1)`

B

`(n (n+1)^(2))/(4)`

C

`(3n(n+1))/(2)`

D

`(n ^(2) (n+1)^(2))/(4)`

Text Solution

Verified by Experts

The correct Answer is:
A
Promotional Banner

Topper's Solved these Questions

  • MCQ's

    CHHAYA PUBLICATION|Exercise QUESTION PAPER 6|90 Videos

  • MCQ's

    CHHAYA PUBLICATION|Exercise QUESTION PAPER 9|66 Videos

  • MCQ's

    CHHAYA PUBLICATION|Exercise QUESTION PAPER 7|90 Videos

  • MCQ ZONE 3

    CHHAYA PUBLICATION|Exercise Question Paper 8|30 Videos

  • Measures of Central Tendency

    CHHAYA PUBLICATION|Exercise Exercise 2 C Very short answer type question|18 Videos

Similar Questions

Explore conceptually related problems

The sum of first n terms of the series a + ar + ar^(2) +…+ ar^(n-1) +… oo is -

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 (n(n+1)^2)/2 when n is even. When n is odd the sum is

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

The sum to n terms of the series [1. (1!)+2. (2!)+ 3.(3!)+…] is-

If the sum of first n terms of a series is 2n^(2) + 3n , find the series.

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

Sum of n terms of the series (2n-1)+2(2n-3)+3(2n-5)+.... is

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 to n terms of each of the series in 1^2 + (1^2 + 2^2) + (1^2 + 2^2 + 3^2) + ...

Find the sum of the first n terms of the series 1^3+3.2^2+3^3+3.4^2+5^2+3.6^2+.... when n is even

CHHAYA PUBLICATION-MCQ's-QUESTION PAPER 8
  1. Solution set of the inequation |(2)/(x-4)| gt 1 (x ne 4) is-

    Text Solution

    |

  2. If the 5th term of a G.P. is x, then the product of its first nine ter...

    Text Solution

    |

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

    Text Solution

    |

  4. If ""^(-3) ^(n)C(r+1) then-

    Text Solution

    |

  5. omega is an imaginary cube root of unity. If (1+ omega ^(2)) ^(m)=(1+o...

    Text Solution

    |

  6. Locus of mid-point of the portionof the line x cos alpha + y sin alpha...

    Text Solution

    |

  7. A ray of light is sent along the lie x-2y+5=0, upon reaching the line ...

    Text Solution

    |

  8. The coordinates of O , A and B are (0,0) , (x,y) and (y,x) respectivel...

    Text Solution

    |

  9. If t is a variable parameter, then the equation to the locus defined b...

    Text Solution

    |

  10. A circel cuts intercepts of lenghts 2a and 2b from the x-axis and the ...

    Text Solution

    |

  11. The ordinate of the centre of the circle passing through (0,0) and (1,...

    Text Solution

    |

  12. The sides of a triangle are 3x+4y, 4x +3y and 5x +5y where, x, y gt 0,...

    Text Solution

    |

  13. The triangle formed by joining the points (x,y,z), (y,z,x) and (z,x,y)...

    Text Solution

    |

  14. The sum of the focal distances of any point on the conic 16x^(2) + 25 ...

    Text Solution

    |

  15. Without rotation of axes if the origin is shifted to the point ((ab)/(...

    Text Solution

    |

  16. The distance between the lines 5x+3y =7 and 15 x +9y +14=0 is-

    Text Solution

    |

  17. The ratio in which he line-segment joining the points (p,q,r) and (-p,...

    Text Solution

    |

  18. The centre of a circel is at (2, -3) and its circumference is 10pi, th...

    Text Solution

    |

  19. If two circles (x-1) ^(2) + (y-3) ^(2) =r^(2)and x ^(2) +y^(2) -8x +2y...

    Text Solution

    |

  20. The lines ax+by+c=0, bx+cy+a =0, cx+ay+b =0 are concurrent when-

    Text Solution

    |