Home
Class 11
MATHS
S(n) = 1^(3) + 2^(3) + 3^(3) + …... + n^...

`S_(n) = 1^(3) + 2^(3) + 3^(3) + …... + n^(3) and T_(n) = 1+ 2 + 3+ 4…...n`

A

`S_(n) = T_(n)^(3)`

B

`S_(n) = T_(n^2) `

C

`S_(n) = T_(n)^(2)`

D

`S_(n) = T_(n)^(3)`

Text Solution

Verified by Experts

The correct Answer is:
C
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

Use mathematical induction to prove that statement 1^(3) + 2^(3) + 3^(3) + . . . + n^(3) = (n^(2) (n + 1)^(2))/( 4) , AA n in N

If 2^(3) + 4^(3) + 6^(3) + … + (2n)^(3) = kn^(2) ( n+1)^(2) then k=

underset(n to oo)lim (1^(3)+2^(3)+3^(3)+...+n^(3))/(n^(4))=

If t_(n) = (1)/(4) (n+2) (n+3) for n=1,2,3….. then (1)/( t_1) + (1)/( t_2) + (1)/( t_3) + ….. + (1)/( t_(2003) )=

AAKASH SERIES-MATHEMATICAL INDUCTION-PRACTICE SHEET (EXERCISE-I) LEVEL-I (Principle of Mathematical Induction) (Straight Objective Type Questions)
  1. (1)/(2) tan"" ((x)/(2) ) + (1)/( 4) (tan"" (x)/(4) ) + ...... + (1)/(2...

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

  6. 1+ (1+3) + (1+3+ 5) + ….n brackets =

    Text Solution

    |

  7. 1+ ((1)/(3) + (1)/(3^2) ) + (( 1)/( 3^3) + (1)/( 3^4) + (1)/( 3^5) ) ...

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

  11. If 'a' and 'b'are natural numbers such that a^(2) - b^(2) is prime num...

    Text Solution

    |

  12. AA n in N, 49^(n) + 16n -1 is divisible by

    Text Solution

    |

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

    Text Solution

    |

  14. Sum of the cubes of three successive natural number is divisible by

    Text Solution

    |

  15. For every natural number n, 3^(2n+2) - 8n -9 is divisible by

    Text Solution

    |

  16. If 10^(n) + 3.4^(n) + x is divisible by 9 for all n in N, then least ...

    Text Solution

    |

  17. AA n in N, 5^(2n+2) - 24n - 25 is divisible by

    Text Solution

    |

  18. If y^(n) -1 is divisible by y+ a for all values of n in N, then a must...

    Text Solution

    |

  19. 7^(13) + 6^(13) is divisible by

    Text Solution

    |

  20. (1+ x)^(n) -nx -1 is divisible by (where n in N )

    Text Solution

    |