Home
Class 11
MATHS
Prove by induction that the integer next...

Prove by induction that the integer next greater than `(3+sqrt5)6n` is divisible by `2^n` for all `nin N`

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

Prove that 2.7^(n)+ 3.5^(n)-5 is divisible by 24 for all n in N

n(gt1) is a positive integer . Show that 14^(n)-13n-1 is divisible by 13 for all n .

Prove by induction that n(n+1)(2n+1) is divisible by 6 for all ninNN .

For every positive integer n, prove that 7^(n) – 3^(n) is divisible by 4.

Using the principle of mathematical induction, prove that (2^(3n)-1) is divisible by 7 for all n in N

For + ve integer n,n^(3)+2n is always divisible by

Prove that (25)^(n+1)-24n+5735 is divisible by (24)^2 for all n=1,2,...

Prove by mathematical induction that for any positive integer n , 3^(2n)-1 is always divisible by 8 .

Using the principle of mathematical induction. Prove that (x^(n)-y^(n)) is divisible by (x-y) for all n in N .

Prove that 33! is divisible by 2^19 and what is the largest integer n such that 33! is divisible by 2^n ?

PATHFINDER-BINOMIAL THEOREM-QUESTION BANK
  1. For ninN, prove that ((n+1)/2)^ngt n!

    Text Solution

    |

  2. Using mathematical induction to show that p^(n+1) +(p+1)^(2n-1) is div...

    Text Solution

    |

  3. Prove by induction that the integer next greater than (3+sqrt5)6n is d...

    Text Solution

    |

  4. Using the principle of mathematical induction show that tan^(-1)(x/(1+...

    Text Solution

    |

  5. Prove by induction that (1+x1)(1+x2)(1+x3)…….(1+xn) ge 1+x1+x2+……+xn

    Text Solution

    |

  6. Use induction to prove that 3^(2n)-1 is not exactly divisible by 2^(n+...

    Text Solution

    |

  7. (x+sqrt(x^3-1))^5+(x-sqrt(x^3-1))^5 is a polynomial of degree

    Text Solution

    |

  8. if the coefficients of x^7 & x^8 in the expansion (2+x/3)^n are equal ...

    Text Solution

    |

  9. The term independent of x in (sqrt(x/3)+sqrt(3/(2x^2)))^10 is

    Text Solution

    |

  10. The total number of terms in the expansion of (x+y)^(100)+(x-y)^(100) ...

    Text Solution

    |

  11. The term independent of x in the expansion of (1+x+2x^3)(3/2(x^2)-1/(3...

    Text Solution

    |

  12. 5th term from the end in the expansion of ((x^3/2)-(2/x^2))^12 is

    Text Solution

    |

  13. The coefficient of x^3 in the expansion of (1-x+x^2)^5 is

    Text Solution

    |

  14. The coefficient of x^4 in the expansion of (1+x+x^2+x^3)^11 is

    Text Solution

    |

  15. The greatest term (numerically) in the expansion of (3-5x)^11 when x=1...

    Text Solution

    |

  16. Which of the following expression is divisible by 1225?

    Text Solution

    |

  17. The value of where ^nCr is

    Text Solution

    |

  18. If the sum of odd numbered terms and the sum of even numbered terms in...

    Text Solution

    |

  19. If P(n)=2+4+6+…..+2n ninN then P(k) =k(k+1) implies P(k+1)=(k+1)(k+2) ...

    Text Solution

    |

  20. The value of the natural numbers n such that the inequality 2^ngt2n+1 ...

    Text Solution

    |