Home
Class 11
MATHS
2+7+14+…..+ (n^(2) + 2n-1)=...

`2+7+14+…..+ (n^(2) + 2n-1)=`

A

`n(2n^(2) + 9n+1))/( 6) `

B

`(2n^(2) + 9n+1)/( 6)`

C

`(2n^(2) + 9n+1)/( 12)`

D

`(2n^(2) + 9n+1)/( 24)`

Text Solution

Verified by Experts

The correct Answer is:
A
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

1 ^(2) + 2^(2) + 3^(2) + . . . + n^(2) = (n (n + 1) (2 n + 1))/( 6)

If alpha in R, n in N " and " n + 2 (n - 1)+ 3 (n-2) + …… +(n-1)2 + n.1 = alpha n ( n + 1) (n + 2) , " then " alpha =

Prove by the method of induction, (1)/( 1.3) + (1)/( 3.5) + (1)/( 5.7) + . . . + (1)/( (2n - 1)(2n + 1)) = (n)/(2 n +1)

2 + 7 + 12 + . . . + (5 n - 3) = (n(5 n -1))/(2)

AA n in , 7^(2n) + 3^(n-1) . 2^(3n-3) is divisible by

If n is a positive integer, prove that 1-2n +(2n(2n-1))/(2!) - (2n(2n-1) (2n-2))/(3!) +… + (-1)^(n-1) (2n(2n-1) …(n+2))/((n-1)!) = (-1)^(n+1) ((2n)!)/(2(n!)^(2))

""^(2n +1)C_0^2 -""^(2n+1)C_1^2 + ""^(2n+1)C_2^2 -…….- ""^(2n+1)C_(2n+1)^2 =

AAKASH SERIES-MATHEMATICAL INDUCTION-PRACTICE SHEET (EXERCISE-I) LEVEL-I (Principle of Mathematical Induction) (Straight Objective Type Questions)
  1. Sum of first 'n' terms of the series = (3)/(2) + (5)/(4) + (9)/(8) + (...

    Text Solution

    |

  2. 0.2 + 0.22 + 0.222+ …. upto n terms is equal to

    Text Solution

    |

  3. 2+7+14+…..+ (n^(2) + 2n-1)=

    Text Solution

    |

  4. 1.6 + 2.9+ 3.12+ ….. + n ( 3n+3)=

    Text Solution

    |

  5. 2.4 + 4.7 + 6.10+ …. upto (n-1) terms=

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

  10. 1 + (x)/( a1) + ( x( x+a1) )/( a1 a2 ) + .... + ( x ( x+a1) (x+ a2)......

    Text Solution

    |

  11. (1)/(2) tan"" ((x)/(2) ) + (1)/( 4) (tan"" (x)/(4) ) + ...... + (1)/(2...

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

  16. 1+ (1+3) + (1+3+ 5) + ….n brackets =

    Text Solution

    |

  17. 1+ ((1)/(3) + (1)/(3^2) ) + (( 1)/( 3^3) + (1)/( 3^4) + (1)/( 3^5) ) ...

    Text Solution

    |

  18. Sum of n^( th) bracket of (1) + (2+ 3+4) + ( 5+ 6+ 7+ 8+9) + ….. is

    Text Solution

    |

  19. { n (n+1) (2n+1) : n in Z} sub

    Text Solution

    |

  20. If a,b and n are natural numbers then a^(2n-1) + b^(2n-1) is divisible...

    Text Solution

    |