Home
Class 11
MATHS
1^(2) + 3^(2) + 5^(2) + …. upto n terms...

`1^(2) + 3^(2) + 5^(2) + ….` upto `n ` terms =

A

`( n (2n-1) (2n+1))/( 6)`

B

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

C

`(n (n+1) (2n+1) )/( 12)`

D

`(n (n+1) (2n-1) )/(6)`

Text Solution

Verified by Experts

The correct Answer is:
B
Promotional Banner

Topper's Solved these Questions

  • MATHEMATICAL INDUCTION

    AAKASH SERIES|Exercise PRACTICE SHEET (EXERCISE-I) LEVEL-I (Principle of Mathematical Induction) (Straight Objective Type Questions)|55 Videos

  • LOCUS

    AAKASH SERIES|Exercise PRACTICE EXERCISE|37 Videos

  • MATRICES

    AAKASH SERIES|Exercise LINEAR EQUATIONS - PRACTICE EXERCISE|15 Videos

Similar Questions

Explore conceptually related problems

2+ 3.2 + 4.2^(2) + …... upto n terms =

The sum (3)/(1^(2)) + (5)/(1^(2) + 2^(2)) + (7)/(1^(2)+ 2^(2) + 3^(2)) + ….. upto 11 terms is

If the sum (3)/(1^(2)) + (5)/(1^(2) + 2^(2)) + (7)/(1^(2) + 2^(2) + 3^(2)) + …+ upto 20 terms is equal to (k)/(21) , then k is equal to

The sum of the series 2^(2) + 2(4^(2)) + 3(6^(2)) + ….upto 10 terms is

1^(3) + 1^(2) + 1+2^(3) + 2^(2) + 2+3^(2) + 3^(2) + 3+3… 3n terms =

(1^(2) )/( 1) + (1^(2) + 2^(2) )/(1+2) + (1^(2) + 2^(2) + 3^(2) )/( 1+ 2+ 3)+ …. + n terms =

AAKASH SERIES-MATHEMATICAL INDUCTION-PRACTICE SHEET (EXERCISE-I) LEVEL-I (Principle of Mathematical Induction) (Straight Objective Type Questions)
  1. If 1+ 5+ 12+ 22 + 35+ ….. + to n terms = ( n^(2) (n+1) )/(2) then n^...

    Text Solution

    |

  2. 1+ 3+ 7 + 15…n terms =

    Text Solution

    |

  3. 1^(2) + 3^(2) + 5^(2) + …. upto n terms =

    Text Solution

    |

  4. 2+ 3.2 + 4.2^(2) + …... upto n terms =

    Text Solution

    |

  5. (1^(2) )/( 1) + (1^(2) + 2^(2) )/(1+2) + (1^(2) + 2^(2) + 3^(2) )/( 1...

    Text Solution

    |

  6. Sum of first 'n' terms of the series = (3)/(2) + (5)/(4) + (9)/(8) + (...

    Text Solution

    |

  7. 0.2 + 0.22 + 0.222+ …. upto n terms is equal to

    Text Solution

    |

  8. 2+7+14+…..+ (n^(2) + 2n-1)=

    Text Solution

    |

  9. 1.6 + 2.9+ 3.12+ ….. + n ( 3n+3)=

    Text Solution

    |

  10. 2.4 + 4.7 + 6.10+ …. upto (n-1) terms=

    Text Solution

    |

  11. sum(n=0)^( oo) (-1)^(n) x^( n+1)=

    Text Solution

    |

  12. sum(k=1)^(2n+1) (-1)^(k-1) k^2 =

    Text Solution

    |

  13. cos theta + cos 2 theta + cos 3 theta + …. + cos { (n-1) theta}+ cos n...

    Text Solution

    |

  14. If P (n) = 1+2+3+ …. + n is a perfect square N^(2) and N is less than...

    Text Solution

    |

  15. 1 + (x)/( a1) + ( x( x+a1) )/( a1 a2 ) + .... + ( x ( x+a1) (x+ a2)......

    Text Solution

    |

  16. (1)/(2) tan"" ((x)/(2) ) + (1)/( 4) (tan"" (x)/(4) ) + ...... + (1)/(2...

    Text Solution

    |

  17. For any integer n ge 1, then sum(k=1)^(n) k ( k+2) is equal to

    Text Solution

    |

  18. S(n) = 1^(3) + 2^(3) + 3^(3) + …... + n^(3) and T(n) = 1+ 2 + 3+ 4….....

    Text Solution

    |

  19. A = sum of first 10 natural numbers, B = sum of squares of first 10 ...

    Text Solution

    |

  20. If sum (r=1)^(n) t(r) = (1)/( 12) n (n+1) (n+2) then sum(r=1)^(n) (1)...

    Text Solution

    |