Home
Class 12
MATHS
If n be a positive integer then prove th...

If n be a positive integer then prove that the integral part P of `(5+2sqrt6)^n` is an odd integer. If `f` be the fractional part of `(5+2sqrt6)^n`, prove that `P=frac{1}{1-f}-f`

Text Solution

AI Generated Solution

Promotional Banner

Topper's Solved these Questions

  • Binomial Theorem for Positive Integrel Index

    A DAS GUPTA|Exercise Exercise|113 Videos

  • Application of dy/dx

    A DAS GUPTA|Exercise Exercise|45 Videos

  • Circles

    A DAS GUPTA|Exercise EXERCISE|122 Videos

Similar Questions

Explore conceptually related problems

If n is positive integer,then prove that the integral part of (7+4sqrt(3))^(n) is an odd number.

Show that the integral part of (5 + 2 sqrt(6))^(n) is odd where n is natural number

Show that the integral part of (5 sqrt(5) + 11)^(2n +1) is even where n in N .

If n be a positive integer, then prove that 6^(2n)-35n-1 is divisible by 1225.

If I is integral part of (2+sqrt(3))^(n) and f is its fractional part.Then (I+f)(1-f) is:

For any positive integer n, prove that n^(3)-n divisible by 6.

Let (6sqrt(6)+14)^(2n+1)=R, if R be the fractional part of R, then prove that Rf=20^(n+1)

For any positive integer n prove that n^(3)-n is divisible by 6

For any positive integer n,prove that n^(3)-n is divisible by 6

A DAS GUPTA-Binomial Theorem for Positive Integrel Index-Exercise
  1. If the four consecutive coefficients in any binomial expansion be a, b...

    Text Solution

    |

  2. Let (1+x^2)^2*(1+x)^n=sum(k=0)^(n+4)ak*x^k If a1, a2 and a3 are iun ...

    Text Solution

    |

  3. If n be a positive integer then prove that the integral part P of (5+2...

    Text Solution

    |

  4. If (9+4sqrt5)^n=p+beta where n and p are positive integers and beta is...

    Text Solution

    |

  5. Integer just greater tehn (sqrt(3)+1)^(2n) is necessarily divisible by...

    Text Solution

    |

  6. The greatest coefficient in the expansion of (1+x)^(2n) is

    Text Solution

    |

  7. If x=1//3, find the greatest tem in the expansion of (1+4x)^8dot

    Text Solution

    |

  8. Find the numerically greatest term in the expansion of (3-2x)^9 when x...

    Text Solution

    |

  9. Find the value of the greatest term in the expansion of sqrt3(1+frac{1...

    Text Solution

    |

  10. In the expansion of (x+a)^15, if the eleventh term is the geometric me...

    Text Solution

    |

  11. In the expansion of (frac{3}{2}+frac{x}{3})^n when x=frac{1}{2} , it i...

    Text Solution

    |

  12. Prove that the greatest coefficient in the expansion of (1+x)^(2n) is...

    Text Solution

    |

  13. Find the sum : ""^(2n+1)C0+""^(2n+1)C1+""^(2n+1)C2+...+""^(2n+1)Cn.

    Text Solution

    |

  14. The sum of the series 1/(1!(n-1)!)+1/(3!(n-3)!)+1/(5!(n-5)!)+…..+1/((n...

    Text Solution

    |

  15. Find the sum :1/2*""^(n)C0+""^(n)C1+2*""^(n)C2+2^2*""^nC3+...+2^(n-1)*...

    Text Solution

    |

  16. Prove that : (1+""^nC1+""^nC2+""^nC3+...+""^nCn)^2=1+""^(2n)C1+""^(2n)...

    Text Solution

    |

  17. If t0,t1, t2,...,tn are the terms in the expansion of (x+a)^n then pro...

    Text Solution

    |

  18. If (1+x-x^2)^10/(1+x^2)=a0+a1x+a2x^2+...+anx^n+… then find a0+a1+a2+….

    Text Solution

    |

  19. If (1+x-x^2)^10/(1+x^2)=a0+a1x+a2x^2+...+anx^n+… then find a0-a1+a2......

    Text Solution

    |

  20. If (1+x-x^2)^10/(1+x^2)=a0+a1x+a2x^2+...+anx^n+… then find a0+a2+a4+…

    Text Solution

    |