Home
Class 11
MATHS
For a positive integer (n gt 1), Let a (...

For a positive integer `(n gt 1)`, Let `a (n) = 1+ (1)/(2) + (1)/(3) + (1)/(4) ….... + (1)/( (2^(n) )-1)` Then

A

`a (100) lt 100`

B

`a ( 100 ) gt 100`

C

`a (20 ) = 100`

D

`a (200) ge 100`

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

Let P(n) : 1+ (1)/(4) + (1)/(9) + …. + (1)/(n^2) lt 2 - (1)/( n) is true for

For all positive integers n gt 1, { x(x^(n-1) - n,a^(n-1) ) } + a^(n) (n-1) } 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))

underset(n to oo)lim {(1)/(1.2)+(1)/(2.3)+(1)/(3.4)+...+(1)/(n(n+1))}=

The lest positive integer n such that 1- (2)/(3)- (2)/(3^(2))- ….- (2)/(3^(n-1)) lt (1)/(100) , is

If n is a positive integer, show that (1 + i)^(n) + (1 - i)^(n) = 2 ^((n+2)/2) cos ((npi)/4) .

Lt_(n rarr oo)[(1)/(3n+1) + (1)/(3n+2)+…+(1)/(4n)]

1/(3 .1!)+(1)/(4.2!) +(1)/((n+2))=. . .

If n is a positive integer then 2^(4n) - 15n - 1 is divisible by

AAKASH SERIES-MATHEMATICAL INDUCTION-PRACTICE SHEET (EXERCISE-I) LEVEL-I (Principle of Mathematical Induction) (Straight Objective Type Questions)
  1. If 'a' and 'b'are natural numbers such that a^(2) - b^(2) is prime num...

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

  9. 7^(13) + 6^(13) is divisible by

    Text Solution

    |

  10. (1+ x)^(n) -nx -1 is divisible by (where n in N )

    Text Solution

    |

  11. For a positive integer (n gt 1), Let a (n) = 1+ (1)/(2) + (1)/(3) + (1...

    Text Solution

    |

  12. For all positive integers n gt 1, { x(x^(n-1) - n,a^(n-1) ) } + a^(n) ...

    Text Solution

    |

  13. ((n+2)!)/( (n-1)!) is divisible by

    Text Solution

    |

  14. When 2^( 301) is divided by 5, the least +ve remainder is

    Text Solution

    |

  15. Statement -1 : For all n in N, x^( 2n+1) +y^(2n+1) is divisible by x+y...

    Text Solution

    |

  16. Statement - 1 : For all n in N x^(n) - y^(n) is divisible by x-y Sta...

    Text Solution

    |

  17. A) 49^(n) + 16n +1 is divisible by A ( n in N) B) 3^(2n) + 7 is divi...

    Text Solution

    |

  18. Let S = (1)/( 1.4) + (1)/( 4.7) + (1)/(7.10) + .....n terms, Observe t...

    Text Solution

    |

  19. The smallest +ve integer n for which n! lt ( (n+1)/( 2) )^(n) holds is

    Text Solution

    |

  20. If n gt 1 then

    Text Solution

    |