Home
Class 11
MATHS
Prove that AA n,14^n-13n-1 is divisible ...

Prove that `AA n,14^n-13n-1` is divisible by 13.`(n in N)`

Promotional Banner

Topper's Solved these Questions

  • MCQ

    UNITED BOOK HOUSE|Exercise EXERCISE|114 Videos

  • MODEL QUESTION PAPERS-SET 10

    UNITED BOOK HOUSE|Exercise EXERCISE|48 Videos

Similar Questions

Explore conceptually related problems

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

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

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

Using binomial theorem, prove that 2^(3n)-7n-1 is divisible by 49 , where n in Ndot

By using mathematical induction prove that 3^(2n)-8n-1 is divisible by 64 when n is an integer.

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

Prove that , 2^(2n)-3n-1 is divisible by 9 for all positive intergral values of n greater than 1 .

Using the principle of mathematical induction prove that 3^(2n+1)+2^(n+2) is divisible by 7 [n in N]

If (10^(2n-1)+1) is divisible by 11, then prove that (10^(2n+1)+1) is also divisible by 11.

Using principle of mathematical induction, prove that 7^(4^(n)) -1 is divisible by 2^(2n+3) for any natural number n.

UNITED BOOK HOUSE-MODEL QUESTION PAPERS-SET 1-EXERCISE
  1. 1st,2nd,and 8th term of a G.P are a^-4,a^m,a^52.Find the value of m.

    Text Solution

    |

  2. If the 5th term of the expansion of (x^(2//3)+x^-1)^nis the term indep...

    Text Solution

    |

  3. Prove that AA n,14^n-13n-1 is divisible by 13.(n in N)

    Text Solution

    |

  4. Find the distance between the lines 3x+4y=9 and 6x+8y+15=0.

    Text Solution

    |

  5. Find the ratio in which the plane 2x+3y+5z=1 divides the line segment ...

    Text Solution

    |

  6. From 1st principle differentiate f(x)=sqrtxwith respect to x.

    Text Solution

    |

  7. If f(x)=1/x (x!=0),Show that f'(1)-f'(-1)=0.

    Text Solution

    |

  8. Show that the SD of two variables is half of their optimum value.

    Text Solution

    |

  9. P(A)=1/2,P(B)=1/3,P(C)=1/4,are these true?when A,B,C are mutually disj...

    Text Solution

    |

  10. For any two sets,prove that n(Acup B)=n(A)+n(B)-n(AcapB).

    Text Solution

    |

  11. If cosec theta+sectheta=cosecalpha+secalpha,then show that tan ((theta...

    Text Solution

    |

  12. Solve :cos^8alpha+sin^8alpha=17/32

    Text Solution

    |

  13. If x=a+b,y=aw+bw^2,z=aw^2+bw,show that xyz=a^3+b^3

    Text Solution

    |

  14. If ,p,q,a,b are 6th,7th,8th and 9th term of the expansion of (x+r)^n,t...

    Text Solution

    |

  15. By using mathematical induction prove that 3^(2n)-8n-1is divisible by ...

    Text Solution

    |

  16. If a,b,c are in G.P and x,y are the arithmetic mean of a and b aand b,...

    Text Solution

    |

  17. Prove that the straight lines ax+by+c=0,bx+cy+a=0and cx+ay+b=0 are con...

    Text Solution

    |

  18. Find the equation of the straight line which divides perepndicularly t...

    Text Solution

    |

  19. If the image of the co-ordinate of a point (x1,y1)is (x2,y2)with respe...

    Text Solution

    |

  20. 3x+y=5 and x+y-1=0 are the equations of two diamters to the circle,whi...

    Text Solution

    |