Home
Class 12
MATHS
The sum of 1^(st) n terms of the series ...

The sum of `1^(st)` n terms of the series
`(1^(2))/(1) + (1^(2) + 2^(2))/(1 + 2) + (1^(2) + 2^(2) + 3^(2))/(1 + 2 + 3) +`..

A

`( n +2)/(3)`

B

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

C

`(n (n-2))/(3)`

D

`(n(n-2))/(6)`

Text Solution

Verified by Experts

The correct Answer is:
B
Promotional Banner

Topper's Solved these Questions

  • KARNATAKA CET 2001

    KCET PREVIOUS YEAR PAPERS|Exercise Mathematics|53 Videos

Similar Questions

Explore conceptually related problems

The sum of first 9 terms of the series : ( 1^(3))/( 1) + ( 1^(3) + 2^(3))/( 1+ 3) + ( 1^(3) + 2^(3) + 3^(3))/( 1+ 3+ 5)+"........." is :

Sum of the n terms of the series 1 . 2^(2)+2 . 3^(2)+3 . 4^(2)+..

The sum of first 9 terms of the series (1^(3))/(1)+(1^(3)+2^(3))/(1+3)+(1^(3)+2^(3)+3^(3))/(1+3+5)+"........" is

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

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

Sum of 10 terms of the series (3)/(1^(2))+(5)/(1^(2)+2^(2))+(7)/(1+2^(2)+3^(2))+.. .

The sum of n terms of the series 1^(2)-2^(2)+3^(2)-4^(2)+5^(2)-6^(2)+... is

The sum of first 10 terms of the series : (x+(1)/( x))^(2) + ( x^(2) + ( 1)/( x^(2)))^(2) + ( x^(3)+ ( 1)/( x^(3)))^(2) + "......" is :

The sum of 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 :

Sum to n terms of the series 1+(1+2)+(1+2+3)+.. ..

KCET PREVIOUS YEAR PAPERS-KARNATAKA 2016-MATHEMATICS
  1. The order and degree of the differential equation [1 + ((dy)/(dx))^(2)...

    Text Solution

    |

  2. If vec a and vec b are unit vectors, then angle between vec a and vec...

    Text Solution

    |

  3. The sum of 1^(st) n terms of the series (1^(2))/(1) + (1^(2) + 2^(2...

    Text Solution

    |

  4. The 11th term in the expansion of (x + (1)/(sqrt(x)))^(14) is

    Text Solution

    |

  5. Suppose veca + vecb + vecc = 0, |veca| = 3, |vecb| = 5, |vecc| = 7, th...

    Text Solution

    |

  6. If a = 3, b = 4, c = 5 each one of veca, vecb & vecc is perpendicular ...

    Text Solution

    |

  7. If the straight lines 2x + 3y - 3 = 0 and x + ky + 7 = 0 are perpendi...

    Text Solution

    |

  8. The rate of change of area of a circle with respect to its radius at r...

    Text Solution

    |

  9. Find the value of tan(pi/8) ?

    Text Solution

    |

  10. Area lying between the curves y^(2) - 2x and y = x is

    Text Solution

    |

  11. If P(A nn B) = (7)/(10) and P(B) = (17)/(20), where P stands for proba...

    Text Solution

    |

  12. The coefficient of variation of two distributions are 60 and 70. The s...

    Text Solution

    |

  13. Two cards are drawn at randrom from a pack of 52 cards. The probabilit...

    Text Solution

    |

  14. IF sin^(-1)x + sin^(-1) y = (pi)/(2), then x^(2) is equal to

    Text Solution

    |

  15. The value of int(2)^(8) (sqrt(10 -x))/(sqrt(x) + sqrt(10) -x)dx is

    Text Solution

    |

  16. Write the converse and contrapositive of the statement " If x ...

    Text Solution

    |

  17. Two dice are thrown simultaneously, the probability of obtaining a tot...

    Text Solution

    |

  18. If A = [{:(cos 2thet,,-sin 2theta),(sin 2theta,, cos 2theta):}] and A ...

    Text Solution

    |

  19. IF A = [{:(3,,1),(-1,,2):}] then A^(2) -5A is equal to

    Text Solution

    |

  20. Find a value of x for which x(hati+hatj+hatk) is a unit vector.

    Text Solution

    |