Home
Class 11
MATHS
For a positive integer n let a(n)=1+1/2+...

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

A

`a(100)le 100`

B

`a(100)gt100`

C

`a(200)le100`

D

`a(200)le100`

Text Solution

Verified by Experts

The correct Answer is:
A, D
Promotional Banner

Topper's Solved these Questions

  • BASIC MATHEMATICS

    PATHFINDER|Exercise QUESTION BANK |266 Videos
  • BINOMIAL THEOREM AND PRINCIPLE OF MATHEMATICAL INDUCTION

    PATHFINDER|Exercise QUESTION BANK|68 Videos

Similar Questions

Explore conceptually related problems

For each positive integer n , let y_n=1/n((n+1)(n+2).....(n+n))^(1/n) For x in R let [x] be the greatest integer less than or equal to x . If (lim)_(n->oo)y_n=L , then the value of [L] is ______.

Show that, if n be any positive integer greater than 1, then (2^(3n) - 7n - 1) is divisible by 49.

If n be a positive integer, then the digit in the unit's place of 3^(2n-1)+2^(2n-1) is -

If n be a positive integer greater than 1, prove that (frac(n+1)(2))^n > n

If a > b and n is a positive integer, then prove that a^n-b^n > n(a b)^((n-1)//2)(a-b)dot

If n and m (ltn) are two positive integers then n(n-1)(n-2)...(n-m) =

If n is a positive integer, show that, (n+1)^(2) + (n+2)^(2) + …+ 4n^(2) = (n)/(6)(2n+1)(7n+1)

For a positive integer n,n(n+1)(2n+1) when divided by 6 leaves the remainder -

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 !)^2dot

If n is a positive integer and U_(n) = (3 + sqrt5)^(n) + (3 - sqrt5)^(n) , then prove that U_(n + 1) = 6U_(n) - 4U_(n -1), n ge 2

PATHFINDER-BINOMIAL THEOREM-QUESTION BANK
  1. When P is a natural number then p^(n+1)+(p+1)^(2n-1) is divisible by

    Text Solution

    |

  2. Let P(n) denote the statement that n^2+n is odd. It is seen that P(n) ...

    Text Solution

    |

  3. For a positive integer n let a(n)=1+1/2+1/3+1/4+….+1/((2^n)-1) Then

    Text Solution

    |

  4. Let S(k) =1+3+5+……+(2k-1)=3+k^2 Then which of the following is true:

    Text Solution

    |

  5. Statement-1 for every natural number nge2 1/sqrt1 +1/sqrt2 +…..+1/sqrt...

    Text Solution

    |

  6. (1+x)^n-nx-1 is divisible by (where n in N)

    Text Solution

    |

  7. Statement-1 : 11^(25) +12^(25) when divided by 23 leaves the remainder...

    Text Solution

    |

  8. The coefficient of x^(53) in the expansion of sum(m=0)^(100) ^100Cm(x-...

    Text Solution

    |

  9. The coefficient of y in the expansion of (y^2+(c/y))^5 is

    Text Solution

    |

  10. The term independent of x in (x^2-(1/x))^9 is

    Text Solution

    |

  11. The coefficients of x^p and x^q in the expansion of (1+x)^(p+q) are

    Text Solution

    |

  12. If x^m occurs in the expansion of (x+(1/x^2))^(2n) then the coefficien...

    Text Solution

    |

  13. Sum of the series 2C0+C1/2 2^2 +C2/3 2^3+………+Cn/(n+1) 2^(n+1)

    Text Solution

    |

  14. The value of nC0. ^nCn +^nC1 . ^nC(n-1)++……..+^nCn . ^nC0

    Text Solution

    |

  15. If (1+x)^(15)=C0+C1x+C2x^2+……..+C(15)x^(15) then ,^15C0^2-^15C1^2+^15C...

    Text Solution

    |

  16. If sn= sum(r=0)^n 1/(^"nCr) and tn=sum(r=0)^n r/("^nCr) then tn/sn is ...

    Text Solution

    |

  17. The fractional part of =(2^(4n))/15 is

    Text Solution

    |

  18. If the fourth term in the expansion of (px+(1/x))^n is independent of ...

    Text Solution

    |

  19. Find the coefficient of x^20 in the expression of (1+x^2)^40(x^2+2+1/x...

    Text Solution

    |

  20. Let n be a positive integer such that (1+x+x^2)^n=a0+a1x+a2x^2+…….+a(2...

    Text Solution

    |